Questions & Answers

Question

Answers

(A). (x – 4)

(B). (x – 5)

(C). (x – 6)

(D). (x – 7)

Answer
Verified

According to the given information we have a quadratic equation i.e. ${x^2} + x - 20$ and (x + 5)

Let (x – p) be another factor of the given quadratic equation ${x^2} + x - 20$

Therefore, $\left( {x + 5} \right)\left( {x-p} \right) = {x^2} + x - 20$

Now using the splitting, the middle term method for the given quadratic equation ${x^2} + x - 20$

$\left( {x + 5} \right)\left( {x-p} \right) = {x^2} + (5 - 4)x - 20$

$ \Rightarrow \left( {x + 5} \right)\left( {x-p} \right) = {x^2} + 5x - 4x - 20$

$ \Rightarrow \left( {x + 5} \right)\left( {x-p} \right) = x\left( {x + 5} \right) - 4\left( {x + 5} \right)$

$ \Rightarrow \left( {x + 5} \right)\left( {x-p} \right) = \left( {x - 4} \right)\left( {x + 5} \right)$

$ \Rightarrow $x – p = x – 4

$ \Rightarrow $x – x = p – 4

$ \Rightarrow $0 = p – 4

$ \Rightarrow $p = 4

Substituting, the value of p in another factor of the given quadratic equation we get

(x – 4)

Therefore, another factor is (x – 4)