Answer

Verified

445.2k+ views

**Hint:**Before attempting this question, one should have prior knowledge about the concept of factorization and also remember to use splitting the middle term method and suppose (x – p) be another factor of a given quadratic equation, using this information can help you to approach the solution of the problem.

__Complete step-by-step answer__: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)

**Hence, option A is the correct option.**

**Note**: In the above problem we came across the term “quadratic equation” which can be explained as the polynomial equation formed by many terms like numbers and variables in the polynomial equation the variable with the highest power defines the numbers of roots the equation can have, for example, if we have a polynomial equation ${x^2} - 2x - 35$ as you can see that this equation has variable x which has the highest power of 2, therefore, this equation will have 2 roots.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

At which age domestication of animals started A Neolithic class 11 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE