Login/Sign Up
12. If $2$ is a root of the quadratic equation $3{{x}^{2}}+px-8=0$ and the quadratic equation $4{{x}^{2}}-2px+k=0$ has equal roots, find the value of $k$.
12. If $2$ is a root of the quadratic equation $3{{x}^{2}}+px-8=0$ and the quadratic equation $4{{x}^{2}}-2px+k=0$ has equal roots, find the value of $k$.
Class 10 | ICSE | Maths | Quadratic Equations | RD Sharma
12. If $2$ is a root of the quadratic equation $3{{x}^{2}}+px-8=0$ and the quadratic equation $4{{x}^{2}}-2px+k=0$ has equal roots, find the value of $k$.

Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring.

Solution:

Given,

$2$ is as root of $3{{x}^{2}}+px-8=0$

So, on substituting $x=2$ the LHS will become zero and satisfy the equation.

⇒ $3{{\left( 2 \right)}^{2}}+p\left( 2 \right)-8=0$

⇒ $12+2p-8=0$

⇒ $4+2p=0$

⇒ $p=-2$

Now, substituting the value of $p$ in the second equation we have

$4{{x}^{2}}-2\left( -2 \right)x+k=0$

⇒ $4{{x}^{2}}+4x+k=0$

It’s given that the above equation has equal roots.

Thus the discriminant, $D=0$

The equation $4{{x}^{2}}+4x+k=0$ is in the form of $a{{x}^{2}}+bx+c=0$

Where $a=4,b=4,c=k$

$D={{b}^{2}}-4ac$

⇒ ${{4}^{2}}-4\left( 4 \right)\left( k \right)=0$

⇒ $16-16k=0$ [dividing by $16$ both sides]

⇒ $k=1$

Therefore, the value of $k$ is $1.$

i

More Material