Question

Factorise by splitting the middle term: t² + 3t - 28​

Answer 1

EXPLANATION.

Factorizes : t² + 3t - 28.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ t² + 7t - 4t - 28 = 0.

⇒ t(t + 7) - 4(t + 7) = 0.

⇒ (t - 4)(t + 7) = 0.

⇒ t = 4  and  t = - 7.

                                                                                                                 

MORE INFORMATION.

Nature of the roots of quadratic expression.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

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

Answer 2

To factorize :  $t^{2} + 3t -28$

Solution :

• According to question we are asked to split the given expression by splitting the middle term .
• We spilt the middle term such that product of the numbers is last term and sum or difference of those numbers is middle term .

• Here , $3t$ is the middle term and $-28$ is the last term  .

• $t^{2} + 3t -28$

      $= t^{2} + 7t -4t -28 \\= t(t +7 ) -4 (t +7)\\= (t -4 ) (t + 7 ) \\t = 4 \ or \ t = -7$

Hence , on splitting the middle term of $t^{2} + 3t -28$ we get value of $t = 4 \ or -7$