Question

If 5 is a root of \[{{x}^{2}}-\left( p-1 \right)x+10=0\], then find the value of ‘p’ is?
a) 4
b) 6
c) 8
d) -8

Answer 1

Hint:In the given question, we have been asked to find the value of ‘p’ in \[{{x}^{2}}-\left( p-1 \right)x+10=0\] and it is given that 5 is the root if this quadratic equation. We use this fact to solve the given question. We substitute x=5 in the given quadratic equation and later simplifying the equation, we will get the required value of ‘p’.

Complete step by step solution:
We have given the quadratic equation,
\[\Rightarrow {{x}^{2}}-\left( p-1 \right)x+10=0\]
It is given that 5 is the root of \[{{x}^{2}}-\left( p-1 \right)x+10=0\] then,
Substitute \[x=5\]in the given quadratic equation
\[\Rightarrow {{x}^{2}}-\left( p-1 \right)x+10=0\]
\[\Rightarrow {{5}^{2}}-\left( p-1 \right)\times 5+10=0\]
Square of 5 is equals to 25, we obtain
\[\Rightarrow \left( 25 \right)-\left( p-1 \right)\times 5+10=0\]
Distribute 5 over the bracket\[\left( p-1 \right)\], we get
\[\Rightarrow \left( 25 \right)-5p+5+10=0\]
Now, solving the above equation for the value of ‘p’
Combining the numbers, we get
\[\Rightarrow 25-5p+15=0\]
\[\Rightarrow 40-5p=0\]
Subtracting 40 from both the sides of the equation, we get
\[\Rightarrow 40-5p-40=0-40\]
On simplifying, we get
\[\Rightarrow -5p=-40\]
Cancelling out the negative sign from both the sides of the equation, we get
\[\Rightarrow 5p=40\]
Dividing both the sides of the equation by 5, we get
\[\Rightarrow p=8\]
Therefore, the value of ‘p’ is equal to 8.
Hence, the option (c ) is the correct answer.

Note: While doing these types of questions, students need to know about the concepts of roots of the quadratic equation. And the important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. . It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.