# Ex.4.4 Q2 Quadratic Equations Solutions - NCERT Maths Class 10

## Question

Find the value of $$k$$ for each of the following quadratic equation , so that they have two equal roots.

(i) $$2x^\text{2}+kx+3=0$$

(ii) $$kx \left(x-2\right)+6=0$$

Video Solution
Quadratic Equations
Ex 4.4 | Question 2

## Text Solution

What is known?

value of $$k.$$

What is Known?

Quadratic equation has equal real roots.

Reasoning:

Since the quadratic equation has equal real roots:

Discriminant $$b^\text{2}-4ac=0$$

Steps:

(i) $$2x^\text{2}+kx+3=0$$

$a= 2,\;b = k,\;c = 3$

\begin{align}{b^2} - 4ac &= 0\\{{(k)}^2} - 4(2)(3) &= 0\\{k^2} - 24 &= 0\\{k^2} &= 24\\k &= \sqrt {24} \\k &= \pm \sqrt {2 \times 2 \times 2 \times 3} \\k& = \pm 2\sqrt 6 \end{align}

(ii) $$kx \left(x-2\right)+6=0$$

$a = k,\;b = - 2k,\;c = 6$

\begin{align}{b^2} - 4ac &= 0\\{{( - 2k)}^2} - 4(k)(6) &= 0\\4{k^2} - 24k &= 0\\4k(k - 6) &= 0\\k = 6 & \qquad k = 0\\\end{align}
If we consider the value of $$k$$ as $$0,$$ then the equation will not longer be quadratic.

Therefore, $$k = 6$$

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