The roots of the quadratic equation $2x^2-3x-1=0$ are $\alpha$ and $\beta$. Write down the val

Question

The roots of the quadratic equation $2x^2-3x-1=0$ are $\alpha$ and $\beta$. Write down the values of $\alpha+\beta$ and of $\alpha\beta$. Without solving the equation, find the value of each of the following.$\dfrac{1}{\alpha^2}+\dfrac{1}{\beta^2}$ $\left(\alpha-\dfrac{1}{\beta^2}\right)\left(\beta-\dfrac{1}{\alpha^2}\right)$ Determine the quadratic equation with integer coefficients which has roots $\alpha-\dfrac{1}{\beta^2}$ and $\beta-\dfrac{1}{\alpha^2}$.

Accepted Answer

(a) $\frac{3}{2},\ -\frac{1}{2}$ (b)(i) $13$ (ii) $\frac{13}{2}$ (c) $2x^2+23x+13=0$

Adjusted roots from fractional sum and product

Adjusted roots from fractional sum and product

Solution:

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