Question

x2 + 2x – 15 factorise by splitting the middle number​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² + 2x - 15.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² + 5x - 3x - 15 = 0.

⇒ x(x + 5) - 3(x + 5) = 0.

⇒ (x - 3)(x + 5) = 0.

⇒ x = 3 and x = -5.

                                                                                                                         

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

Question:-

• x² + 2x – 15 factorise by splitting the middle number.

To Find:-

• Factorise by splitting method.

Solution:-

$\sf\longrightarrow \: { x }^{ 2 } + 2x - 15 = 0$

$\sf\longrightarrow \: { x }^{ 2 } + 5x - 3x - 15 = 0$

$\sf\longrightarrow \: x( x + 5 ) - 3( x + 5 ) = 0$

$\sf\longrightarrow \: ( x - 3 ) ( x + 5 ) = 0$

$\sf\longrightarrow \: x = 3 , - 5$

Hence ,

• The value of x is 3 , - 5

More to Know:-

Nature of Roots:-

ax² + bx + c = 0 where a , b , c ∈ R

• ∆ > 0 . Then the roots are real and distinct.

• ∆ = 0 . Then the roots are real and equal.

• ∆ < 0 . Then the roots are complex.