Question

Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (i) $2 x^{2}+k x+3=0$ (ii) $k x(x-2)+6=0$

Name: Problem 2, Chapter 4: NCERT Class 10 - Math
Uploaded: 2021-07-06T16:20:35-08:00
Duration: 3 min 20 s
Channel: Faizanullah Kazmi
Description: Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2 x^2+k x+3=0 (ii) k x(x-2)+6=0

   Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots.
(i) $2 x^{2}+k x+3=0$
(ii) $k x(x-2)+6=0$

NCERT Class 10 - Math

Parvin Sinclair,… 1st Edition

Chapter 4, Problem 2

Instant Answer

Solved by Expert Faizanullah Kazmi

07/06/2021

Step 1

The discriminant is given by the formula $D = B^2 - 4AC$. Show more…

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Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (i) $2 x^{2}+k x+3=0$ (ii) $k x(x-2)+6=0$

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a is nonzero. It is a fundamental element in algebra, and understanding its structure is key to exploring various methods of solving equations and analyzing their properties.

Discriminant

The discriminant is the part of the quadratic formula under the square root, expressed as b² - 4ac. It plays a crucial role in determining the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, there is one repeated real root; and if negative, the roots are complex conjugates.

Equal (Double) Roots Condition

For a quadratic equation to have two equal (double) roots, the discriminant must be exactly zero. Setting b² - 4ac = 0 yields a condition on the parameters of the equation that must be satisfied to ensure that the quadratic has a single unique solution repeated twice.

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