Mathematics: Math Finding the root (30points)

Math Finding the root (30points) - id3010418002, evere11605

genesisprieto11

17.03.2022

p = $\frac{12}{7}$

Step-by-step explanation:

let the root be α then the other root is 3α

The sum of the roots of a quadratic equation is

α + 3α = - $\frac{b}{a}$ = - $\frac{-8}{7}$ = $\frac{8}{7}$

Thus 4α = $\frac{8}{7}$ ( divide both sides by 4 )

α = $\frac{2}{7}$

The product of the roots of a quadratic equation are

α × 3α = $\frac{c}{a}$ = $\frac{p}{7}$ , that is

3α² = $\frac{p}{7}$ ← substitute value of α

3 × ( $\frac{2}{7}$ )² = $\frac{p}{7}$

3 × $\frac{4}{49}$ = $\frac{p}{7}$

$\frac{12}{49}$ = $\frac{p}{7}$ ( cross- multiply )

49p = 84 ( divide both sides by 49 )

p = $\frac{84}{49}$ = $\frac{12}{7}$

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