The roots of the quadratic equation $2{{x}^{2}}-hx+h=0$ (where $h0$) are $\alpha $ an

Question

The roots of the quadratic equation $2{{x}^{2}}-hx+h=0$ (where $h>0$) are $\alpha $ and $\beta $, while those of the equation $25{{x}^{2}}-5x+4=0$ are $\frac{1}{{{\alpha }^{2}}}$ and $\frac{1}{{{\beta }^{2}}}$. Find the value of $h$. Enrichment note: the roots in this question are allowed to be complex. Use the sum and product of roots algebraically; do not assume that the roots are real.

Accepted Answer

$h=5$ (complex-root enrichment).

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Solution:

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