Login/Sign Up
Home » If is a root of the equation . find the value of for the which the quadratic equation has equal roots.
If -4 is a root of the equation x^{2}+2 x+4 p=0. find the value of k for the which the quadratic equation x^{2}+p x(1+3 k)+7(3+2 k)=0 has equal roots.
CBSE | Class 10 | Exercise 10D | Maths | Quadratic Equations | RS Aggarwal
If -4 is a root of the equation x^{2}+2 x+4 p=0. find the value of k for the which the quadratic equation x^{2}+p x(1+3 k)+7(3+2 k)=0 has equal roots.

It is given that -4 is a root of the quadratic equation x^{2}+2 x+4 p=0

\begin{array}{l} \therefore(-4)^{2}+2 \times(-4)+4 p=0 \\ \Rightarrow 16-8+4 p=0 \\ \Rightarrow 4 p+8=0 \\ \Rightarrow p=-2 \end{array}

The equation x^{2}+p x(1+3 k)+7(3+2 k)=0 has real roots.

\begin{array}{l} \therefore D=0 \\ \Rightarrow[p(1+3 k)]^{2}-4 \times 1 \times 7(3+2 k)=0 \\ \Rightarrow[-2(1+3 k)]^{2}-28(3+2 k)=0 \\ \Rightarrow 4\left(1+6 k+9 k^{2}\right)-28(3+2 k)=0 \\ \Rightarrow 4\left(1+6 k+9 k^{2}-21-14 k\right)=0 \\ \Rightarrow 9 k^{2}-8 k-20=0 \\ \Rightarrow 9 k^{2}-18 k+10 k-20=0 \\ \Rightarrow 9 k(k-2)+10(k-2)=0 \\ \Rightarrow(k-2)(9 k+10)=0 \\ \Rightarrow k-2=0 \text { or } 9 k+10=0 \\ \Rightarrow k=2 \text { or } k=-\frac{10}{9} \end{array}

Hence, the required value of k is 2 or -\frac{10}{9}.

i

More Material