Question

18x²-27x-26 Resolve it into factores​

Answer 1

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${18} \times ^{2} - 27 \times - 26 = \\ 18 \times ^{2} = 32 \\ = 32 - 27 \\ = 5 \\ = 5 \times (- 26) \\ = - 21$

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-21

Answer 2

Given :

The given quadratic equation is 18x²-27x-26=0

• a=18

•b=-27

•c=-26

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To Find :

• The roots of the quadratic equation =?

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Formulas :

•For finding determinant value we use determinant method :

$\red \bigstar \boxed{ \sf{ \delta \: d = {b}^{2} - 4ac }}$

•For finding the roots of the quadratic equation we use formula method :

$\red \bigstar \boxed{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}}}$

Solution :

Given, Quadratic equation is 18x²-27x-26=0

Here,

•a=18

•b=-27

•c=-26

By using Factorization method :

$\implies \bf \: 18 {x}^{2} - 27x - 26 = 0$

• Rewrite the polynomial splitting the middle term using the two factors -39 and 12.

$\\ \implies \sf \: 18 {x}^{2} - 27x - 26 = 0 \\ \\ \implies \sf \: 18 {x}^{2} - 39x + 12x - 26 = 0 \\ \\ \implies \sf \: 18 {x}^{2} - 39x + 12x - 26 = 0 \\ \\ \implies \sf \: 3x(6x - 13) + 2(6x - 13) = 0 \\ \\ \implies \sf \: (6x - 13)(3x + 2) = 0 \\ \\ \implies \sf \: 6x = 13 \: \: \quad \: \: 3x = - 2 \\ \\ \implies \sf \: x = \frac{13}{6} \: \: \quad \: or \: \: \: \: x = \frac{ - 2}{3} \\ \\ \implies \boxed{ \sf{x = \frac{13}{6} }} \: \quad \sf or \: \boxed{\sf{x = \frac{ - 2}{3} }}$

The roots of the given quadratic equation is

$\\ \blue\bigstar\boxed{\sf{x=\dfrac{13}{6} \: and \: \: x=\dfrac{-2}{3}}}$