Question

If -5is a root of eq.2x^2+px-15=0 and quadratic equation p(x^2+x)k has equal roots find k

Answer 1

k=0 is the answer of above question

Answer 2

Answer:

The value of k is $k=\frac{7}{4}$.

Step-by-step explanation:

The given equation is

$2x^2+px-15=0$

It is given that -5 is a root of this equation. It means x=-5 must satisfy the equation.

$2(-5)^2+p(-5)-15=0$

$50-5p-15=0$

$5p=35$

$p=7$

The value of p is 7.

The another equation is

$P(x)=p(x^2+x)+k$

$P(x)=7(x^2+x)+k$

$P(x)=7x^2+7x+k$

It is given that this equation has equal roots. The sum of roots is -b/a.

$x+x=\frac{-7}{7}$

$2x=-1$

$x=\frac{-1}{2}$

The product of roots is c/a.

$x\times x=\frac{k}{7}$

$x^2=\frac{k}{7}$

$(\frac{-1}{2})^2=\frac{k}{7}$

$k=\frac{7}{4}$

Therefore the value of k is $k=\frac{7}{4}$.