The roots of the quadratic equation $5{{x}^{2}}+x+2=0$ are $\alpha $ and $\beta $. Find the qu

Question

The roots of the quadratic equation $5{{x}^{2}}+x+2=0$ are $\alpha $ and $\beta $. Find the quadratic equations whose roots are $3\alpha $ and $3\beta $ $\frac{1}{\alpha }$ and $\frac{1}{\beta }$ $\frac{1-\alpha }{\alpha }$ and $\frac{1-\beta }{\beta }$ 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

Enrichment with complex roots. (i) $5x^2+3x+18=0$. (ii) $2x^2+x+5=0$. (iii) $2x^2+5x+8=0$.

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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