Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects

Mathematics

Roots of a Quadratic Equation

द्विघात समीकरण के मूल

Roots of a Quadratic Equation, taught in Class 10 Mathematics under the chapter Quadratic Equations, introduces the values of the variable that make a quadratic expression equal to zero. Students learn to identify roots, verify them by substitution, and connect the sum and product of the roots with the coefficients. The topic also helps them form a quadratic equation when its roots are known and use these relationships to solve and check mathematical problems.

Practice questions

If (\alpha) and (\beta) are roots of (3x^2-4x-4=0), what is the value of (\frac{1}{\alpha}+\frac{1}{\beta})?MediumLevel 31If substituting (x=a) in a quadratic equation (p(x)=0) gives (p(a)=0), what is (a) called?MediumLevel 32Is \(x=4\) a root of the equation \(x^2-9x+20=0\)?MediumLevel 32Is x = -2 a root of the equation 3x² + 2x - 8 = 0?MediumLevel 32What are the roots of the quadratic equation \(x^2-12x+35=0\)?MediumLevel 32What are the roots of the equation \(3x^2-13x+4=0\)?MediumLevel 32What are the roots of the equation \(2x^2+9x+4=0\)?MediumLevel 32Which quadratic equation has −3 and 6 as its roots?MediumLevel 32If \(3\) is a root of the equation \(x^2+kx-18=0\), what is the value of \(k\)?MediumLevel 32What is the sum of the roots of the quadratic equation \(4x^2-11x+7=0\)?MediumLevel 32What is the product of the roots of the equation \\(5x^2+6x-8=0\\)?MediumLevel 32What is the discriminant \(D\) of the equation \(3x^2-6x+3=0\)?MediumLevel 32Which statement correctly describes the real roots of the equation \(x^2-4x+13=0\)?MediumLevel 32If the sum of the roots of a monic quadratic equation is 5 and their product is 6, which of the following equations can have those roots?MediumLevel 32If the sum of the roots of a quadratic equation is 9 and their product is 18, which monic quadratic equation is formed?MediumLevel 32One root of the equation \(x^2-15x+54=0\) is \(6\). What is the other root?MediumLevel 32If (3\alpha) and (3\beta) are new roots and (\alpha+\beta=4), what is the sum of the new roots?MediumLevel 32If the roots are (\alpha) and (\beta) with (\alpha+\beta=7) and (\alpha\beta=12), what is (\alpha^2+\beta^2)?MediumLevel 32If the roots of a quadratic equation are (2) and (-7), what is the value of (\frac{1}{\alpha}+\frac{1}{\beta})?MediumLevel 32For (3x^2-14x+8=0), what are the sum and product of roots respectively?MediumLevel 32

Add Muft Shiksha to your Home Screen

In Safari, tap Share, then Add to Home Screen.