Manipur Board Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE 5.1

If $\alpha , \beta$are the roots of the equation $x^2+px+q=0, q\ne 0$ then form the quadratic equation whose roots are

${\alpha }^3,{\beta }^3$

Find the value of $p$ so that the equation $3p{x}^2-12x+p=0$ has equal roots

One root of $x^2+ax-21=0$ is $3$, while $x^2+ax+b=0$ has equal roots. Find $b$.

If one root of the equation $2x^2-5x+k=0$ be reciprocal of the other, find the value of $k$

Find the quadratic equation whose roots are each less by $2$ than those of $x^2-3x+1=0$

If one root of the equation $x^2-px+q=0$ be twice the other, show that $2p^2=9q$.

If one root of the equation $x^2+px+q=0$ be the square of the other, then show that $p^3+q^2+q=3pq$

If the sum of the roots of the equation $\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}$ is zero, prove that the product of the roots is $-\frac{1}{2}(a^2+b^2)$.