10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If the sum of the zeroes of the polynomial \[p(x)=({{p}^{2}}-23){{x}^{2}}-2x-12\] is 1, then p takes the value(s):

A) \[\sqrt{23}\]

B) \[-23\]

C) \[2\]

D) \[\pm 5\]

Correct Answer: D

Solution :

[d] Let \[\alpha \] and \[\beta \] be the zeroes of the polynomial

\[p(x)=({{p}^{2}}-23){{x}^{2}}-2x=12.\]

Then \[\alpha +\beta =-\frac{(-2)}{{{p}^{2}}-23}=\frac{2}{{{p}^{2}}-23}\]

Also, sum of zeroes \[\alpha +\beta =1\] [Given]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,{{p}^{2}}-23=2\Rightarrow {{p}^{2}}-25\Rightarrow p=\pm 5\]