Question

Find the roots by factorizatio
1) under root 2x^2 + 7x + 5 under root
2) x^2 - 3x - 10
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Answer 1

1. $\bold{\sqrt{2}{x}^{2} + 7x + 5\sqrt{2} = 0}$

To find the roots

$\implies \sqrt{2}{x}^{2} + 5x + 2x + 5\sqrt{2} = 0 \\ \implies x(\sqrt{2}x + 5) + \sqrt{2}(\sqrt{2}x + 5 = 0 \\ \implies (\sqrt{2}x + 5)(x + \sqrt{2}) = 0$

$\sqrt{2}x + 5 = 0 \\ x = \dfrac{-5}{\sqrt{2}}$

$x + \sqrt{2} = 0 \\ x = -\sqrt{2}$

Roots of $\sqrt{2}{x}^{2} + 7x + 5 = 0$ are $\dfrac{-5}{\sqrt{2}}$ and $-\sqrt{2}$

2. $\bold{{x}^{2} - 3x - 10}$

To find the roots

$\implies {x}^{2} - 5x + 2x - 10 = 0 \\ \implies x(x-5) +2(x-5) = 0 \\ \implies (x-5)(x+2) = 0$

x - 5 = 0

x = 5

x + 2 = 0

x = -2

Roots of ${x}^{2} - 3x - 10$ are 5 and -2