If - 3 is root of quadratic equation 2xsquare +px-15=0 and quadratic equation p(x square +x) +k=0 has equal roots - Maths - Quadratic Equations

Question

If - 3 is root of quadratic equation 2xsquare +px-15=0 and
quadratic equation p(x square +x) +k=0 has equal roots then find
the value of k ?

Lovina Kansal · Accepted Answer

Let f(x)=2x2+px-15 and g(x)=px2+px+k=0Since -3 is a root of f(x)
So, f(-3)=0⇒2(-3)2+p(-3)-15=0⇒18-3p-15=0⇒3-3p=0⇒3(1-p)=0⇒1-p=0⇒p=1    
(1)Also,-3 is a root of g(x)So, g(-3)=0⇒(1)(-3)2+(1)(-3)+k=0    using 1⇒9-3+k=0⇒6+k=0⇒k=-6

If - 3 is root of quadratic equation 2xsquare +px-15=0 and quadratic equation p(x square +x) +k=0 has equal roots then find the value of k.?