Answered: "Factoring is used to solve quadratics of the..."

High School
Algebra
Algebra I
Quadratic function and equation

Harlen Pritchard

Answered question

2021-02-11

Factoring is used to solve quadratics of the form

a x^{2} + b x + c = 0

when th eroots are rational. Find the roots of the following quadratic functions by factoring:
a)

f (x) = x^{2} - 5 x - 14

f (x) = x^{2} - 64

f (x) 6 x^{2} + 7 x - 3

Answer & Explanation

Alix Ortiz

Skilled2021-02-12Added 109 answers

a) $f (x) = x^{2} - 5 x - 14$
$f (x) \Rightarrow x^{2} - 5 x - 14 = 0$
$x^{2} - 7 x + 2 x - 14 = 0$
$x (x - 7) + 2 (x - 7) = 0$
$(x + 2) (x - 7) = 0$
Hence, the roots are $x = - 2, 7$
b) $f (x) = x^{2} - 64$
$f (x) = 0 \Rightarrow x^{2} - 64 = 0$
$(x - 8) (x + 8) = 0$
Hence, the roots are $x = - 8, 8$
c) $f (x) 6 x^{2} + 7 x - 3$
$f (x) = 0 \Rightarrow 6 x^{2} + 7 x - 3 = 0$
$6 x^{2} + 9 x - 2 x - 3 = 0$
$3 x (2 x + 3) - 1 (2 x + 3) = 0$
$(3 x - 1) (2 x + 3) = 0$
Hence, the roots are $x = - \frac{1}{3}, - \frac{3}{2}$

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