J P Mohindru and Bharat Mohindru Solutions for Chapter: Polynomials, Exercise 1: EXERCISE

If $\alpha$, $\beta$ are the zeroes of the polynomial $p\left(x\right)=3x^2-2x-6$, then find $\frac{1}{\alpha }+\frac{1}{\beta }$.

If $\alpha$, $\beta$ are the zeroes of the polynomial $p\left(x\right)=3x^2-2x-6$, then find ${\alpha }^2+{\beta }^2$.

If $\alpha$, $\beta$ are the zeroes of the polynomial $p\left(x\right)=3x^2-2x-6$, then find ${\alpha }^3+{\beta }^3$.

If $\alpha$, $\beta$ are zeroes of the polynomial $5x^2+2x-3$, then prove that $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=-\frac{34}{15}$.

If $\alpha$, $\beta$ are zeroes of $x^2-3x+1$, then find a polynomial whose zeroes are $\frac{\alpha }{\beta }$, $\frac{\beta }{\alpha }$.

If $\alpha$, $\beta$ are zeroes of $3x^2-4x+1$, then form a polynomial whose zeroes are $\frac{{\alpha }^2}{\beta }$, $\frac{{\beta }^2}{\alpha }$.

If squared difference of the zeroes of the polynomial $x^2+ax+45$ is equal to $144$, then find $a$.

If $\alpha$, $\beta$ are zeroes of the polynomial $x^2+8x+6$, then prove that a quadratic polynomial whose zeroes are $1+\frac{\beta }{\alpha }$, $1+\frac{\alpha }{\beta }$ is $3x^2-32x+32$.