x^2+8x+7=0 ⇒ #160; x^2+7x+x+7=0 ⇒ #160; x(x+7)+1(x+7)=0 ⇒ #160; (x+7)(x+1)=0 ⇒ #160; x+7=0 and x+ ...

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Solve: x2+8x...

Question

Solve:
$x^{2} + 8 x + 7$ =0.

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Solution

$x^{2} + 8 x + 7 = 0$
$\Rightarrow$ $x^{2} + 7 x + x + 7 = 0$
$\Rightarrow$ $x (x + 7) + 1 (x + 7) = 0$
$\Rightarrow$ $(x + 7) (x + 1) = 0$
$\Rightarrow$ $x + 7 = 0$ and $x + 1 = 0$
$∴$ $x = - 7$ and $x = - 1$

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\frac{x^{2} - 8 x + 7}{4 x^{2} - 4 x + 1} < 0

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\Rightarrow 8 x = - 7 + 0

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