Question

In each of the following, find the value of k for which the given value is a solution of the given equation:

(i) $7x^2+kx-3=0,x=\frac{2}{3}$
(ii) $x^2-x\left(a+b\right)+k=0,x=a$
(iii) $k{x}^2+\sqrt{2}x-4=0,x=\sqrt{2}$
(iv) $x^2+3ax+k=0,x=-a$

Answer 1

In each of the following cases find k.

(i) We are given here that,

Now, as we know that is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting in the above equation gives us,

Hence, the value of .

(ii) We are given here that,

Now, as we know that is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting in the above equation gives us,

Hence, the value of .

(iii) We are given here that,

Now, as we know that is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting in the above equation gives us,

Hence, the value of.

(iv) We are given here that,

Now, as we know that is a solution of the quadratic equation, hence it should satisfy the equation. Therefore substituting in the above equation gives us,

Hence the value of.