Question

If the value of a polynomial \[{{x}^{2}}-mx+7\] is \[35\], when \[x=2\] then find m.
A. \[m=2\]
B. \[m=-12\]
C. \[m=-2\]
D. \[m=7\]

Answer 1

Hint: The quadratic equation is given and one of the values of x is also given, so for this type of problem to solve we have to substitute the value of x and solve the equation and find the value of x. Substitute \[x=2\] in \[{{x}^{2}}-mx+7\]= 35 and get the value of m.

Complete step-by-step solution -
Given equation is \[{{x}^{2}}-mx+7=35\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
This is a quadratic equation.
Given \[x=2\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Substitute (2) in (1) we get,
\[{{2}^{2}}-2m+7=35\]
By further solving we get,
\[4-2m+7=35\]
By further solving we get,
\[-2m=35-11\]
By further solving we get,
\[2m=-24\]
By further solving we get,
\[m=-12\].
Therefore the answer is option B.

Note: This is a direct problem. We get the solution just by substituting the given value and doing some mathematical operations. As the problem is easy to solve but take care during calculation.