The roots of the quadratic equation $2{{x}^{2}}-3x+8=0$ are $\alpha $ and $\beta $. Find the q

Question

The roots of the quadratic equation $2{{x}^{2}}-3x+8=0$ are $\alpha $ and $\beta $. Find the quadratic equations whose roots are $5\alpha $ and $5\beta $ $\alpha +2\beta $ and $\beta +2\alpha $ $\frac{\beta }{\alpha }$ and $\frac{\alpha }{\beta }$ 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

Complex-root enrichment. (i) $2x^2-15x+200=0$. (ii) $2x^2-9x+17=0$. (iii) $16x^2+23x+16=0$.

Forming a Quadratic Equation with Given Roots

Forming a Quadratic Equation with Given Roots

Solution:

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