Question

factorise x^2-4x-32 plz plz answer fast ⏩⏩⏩⏩⏩⏩​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² - 4x - 32.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² - 8x + 4x - 32 = 0.

⇒ x(x - 8) + 4(x - 8) = 0.

⇒ (x + 4)(x - 8) = 0.

⇒ x = -4 and x = 8.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \: Solution...}}}}}$

Explaination: The question says that we have to factorise the given expression that is ${\pmb{\sf{\red{x^{2}-4x-32}}}}$ Let us factorise this expression by using middle term splitting method. Let us solve this question!

${\sf{:\implies x^{2}-4x-32}}$

${\sf{:\implies x^{2}-8x+4x-32}}$

${\sf{:\implies x(x) - (-2 \times -2 \times -2) +4(x) - (8)}}$

${\sf{:\implies x(x) - (4 \times -2) +4(x) - (8)}}$

${\sf{:\implies x(x) - 8 +4(x) - (8)}}$

${\sf{:\implies x(x-8) +4(x-8)}}$

${\sf{:\implies (x-8) \: or \: (x+4) = 0}}$

${\sf{:\implies x = 0+8 \: or \: x = 0-4}}$

${\sf{:\implies x = 8 \: or \: x = -4}}$

The value of x we get is 8 or -4.

• Henceforth, factorised!

${\large{\pmb{\sf{\underline{AdditioNal \; Knowledge...}}}}}$

Some knowledge about Quadratic Equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ Discriminant is given by b²-4ac

Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

★ D > 0 then roots are real and distinct.

★ D = 0 then roots are real and equal.

★ D < 0 then roots are imaginary.

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