This page walks you through one of those important NCERT Exemplar problems—the kind that shows up more often than you'd think—and breaks down the full, step-by-step solution. It’s pulled straight from the Class 10 Maths chapter on Quadratic Equations. So if your concepts are a little shaky, or you just want to lock things in before the board exam, this is a solid place to start. Go through it carefully. You'll see the pattern behind these questions much more clearly.
Straight to the point—this question’s all about figuring out what kind of roots that quadratic equation has. Real ones, equal ones, or maybe a pair of imaginary. We’re digging right into that.
Here we have provided NCERT Exemplar Questionfor Class 10 Maths in hindi Language, Just select the chapters below to get Exemplar Solution of the same:
Yeh sawaal Class 10 Maths ke NCERT Exemplar book, Chapter 4 'Quadratic Equations' se uthaya gaya hai. Board exams mein iska poochna aam baat hai, aur concept bhi koi halka nahi hai — kaafi important hai.
Straight to the point here. The question asks us to figure out what kind of roots this quadratic has, and if they’re real, go ahead and find them. The equation in question is 2x² − 6x + 3 = 0. So, we just need to check the discriminant first, and then solve accordingly.
Arre, isko todna hai? Chalo, seedha step-by-step chalte hain—kisi shortcut ki zaroorat nahi, bas focus rakho aur aage badho. Pehle thoda saans lo, phir aaram se har step ko samajhte hue solve karo. Tension nahi, bhai—bas ek ek karke kaam karo, aur dekho kaise answer khud hi mil jaata hai.
Yahan equation hai: 2x² - 6x + 3 = 0. Isko standard form, yani ax² + bx + c = 0, ke saath match karo toh seedha seedha coefficients mil jaate hain. a = 2, b = -6, aur c = 3. Bas, yahi pehla step hai — teeno numbers ko alag karke pehchan lena.
So here’s the deal—you’re hunting for the discriminant, and the formula is D = b² - 4ac. Plug in your numbers: b is -6, a is 2, and c is 3. That gives you D = (-6)² - 4 × 2 × 3. Work it out, and you get 36 minus 24, which lands you at D = 12. Clean, right? That’s your D right there.
Since D is greater than zero — meaning it’s positive — here’s what that tells us about the roots. They’re real, they’re distinct, and they’re unequal. So yeah, exactly two of them. No repeats, no imaginary stuff. Just two clean, separate solutions.
Quadratic formula yahi hai: x = [-b ± √D] / 2a. Ab yahan values daal do — b hai 6, a hai 2, aur D humne pehle nikala tha 12. Toh equation banegi: x = [6 ± √12] / (2 × 2) — denominator simple hai, 4 aayega. Aur √12 ko tod do toh milta hai 2√3. Isliye upar likho: x = [6 ± 2√3] / 4. Ab dono terms ko 2 se kaat do — andar aur bahar. Jo bachta hai woh final answer hai: x = [3 ± √3] / 2. Bas, roots mil gayi.
So, after plugging everything in, you get these two roots: x₁ equals (3 + √3) over 2, and x₂ is (3 - √3) over 2. That's it. Clean, simple, and done.
Real and distinct, plain and simple. The two roots come out to (3 + √3)/2 and (3 - √3)/2 — no repeats, no messy surprises there.
Honestly, this question is a bit of a gift for board exam prep, and here’s why. First, it forces you to actually apply the discriminant and the quadratic formula, not just stare at them. You’re using both in one go, which is exactly the kind of practical drill that sticks. Then there’s the whole idea of roots—whether they’re real, equal, or imaginary—and this one little problem makes that click in a way that reading notes never will. And let’s be real, questions like this show up in CBSE papers all the time, so you’re basically training for the real thing. The best part? If you write your solution step by step, you bank full marks even if you slip up at the very end. That’s how the marking works, so why not use it to your advantage?
Sign mistake: jab b = -6 ho, toh usko square karte waqt sign ka khel samajhna zaroori hai. Logon ko aksar yahan chook lag jaati hai. Calculation error: 4ac nikalte waqt 4 × 2 × 3 = 24, yeh seedha sa hisaab hai, lekin phir bhi log galti kar dete hain. Thoda ruk kar double-check karo. Simplification: √12 = 2√3, isko simplify karna mat bhoolna. Warna answer adhoora reh jayega. Final answer: Roots ko hamesha simplest form mein likho. Yeh chhota sa step hai, par exam mein pura score dilata hai.
Alright, so here’s your first one. Just figure out what kind of roots this equation has: 3x² - 4√3x + 4 = 0. No need to actually solve it—just tell me if they’re real, imaginary, equal, that sort of thing. Next up, if the roots are real, go ahead and find them for x² + 7x + 10 = 0. You know the drill, factor or use the formula, whichever you like. And lastly, check whether the roots are equal for 2x² - 3x + 5 = 0. Quick look at the discriminant should settle it. That’s it—three quick checks to see where you stand.
Discriminant? That’s D = b² - 4ac. Simple enough. Now, what does D actually tell you? If D’s positive, you’ve got two real roots that are distinct. If D’s zero, they’re real but equal—same root twice. And if D’s negative? No real roots at all. That’s it. For the heavy lifting, use the quadratic formula: x equals negative b, plus or minus the square root of D, all over 2a. And don’t forget the standard form underneath everything: ax² + bx + c = 0, with a not equal to zero—otherwise it’s not even quadratic.
So here’s how the marks actually break down when you tackle a question like this in the board exam. You get one mark just for putting the right formula down—that’s step one. Another mark lands for getting the discriminant calculated properly. Then, once you’ve got that number, you need to say whether the roots are real, equal, imaginary, whatever—that’s your third mark. And of course, actually solving for the roots themselves earns you another point. Finally, the big one: writing that final answer clearly gets you the last mark. Simple enough, right? Five marks total, each step counts.
Five marks is five marks, right? So you can't just skip steps or assume the checker will fill in the blanks. Every single step has to be written out properly, no shortcuts. Miss one line, and that's marks gone. Simple as that.
Write the equation down first, and I mean really write it out clearly. Don’t skip that step—rushing past it leads to messy mistakes later. Next, make sure you’ve got the right coefficients: a, b, and c. It sounds basic, but mixing up signs here is the easiest way to throw off everything else. Now for the discriminant. Calculate it slowly, double-check each sign. One tiny slip—like dropping a negative—and the whole nature of your roots changes. So be careful. From there, use D to decide what you’re dealing with. Two real roots — one? None? That tells you which path to take. And here’s a big one: only reach for the quadratic formula when D is zero or positive. If it’s negative, stop right there—you’re heading into imaginary territory, and the formula won’t help you. Once you’ve got your answer, don’t just leave it messy. Simplify it properly — combine terms, reduce fractions, clean it up. A half-finished answer is a half-right answer. Finally, plug your solution back into the original equation. Seriously, do it. It takes thirty seconds and catches most of your errors before they cost you marks. Trust me—this check is worth more than you think.
NCERT Exemplar ke questions ko solve karke aap Quadratic Equations chapter mein ek alag hi confidence aa jaata hai. Aur dekho, board exams mein aise sawaal aksar poochhe jaate hain — toh inka solution acchi tarah samajhna mat bhoolna. Yehi woh cheez hai jo aapko baaki students se aage le jaayegi.
