10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f(t)={{t}^{2}}-4t+3,\] then the value of \[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is:

A) 104

B) 108

C) 122

D) 5

Correct Answer: B

Solution :

[b] Given, \[f(t)={{t}^{2}}-4t+3\]

\[\therefore \] Sum of zeroes \[=\alpha +\beta =4\]

and product of zeroes \[=\alpha \beta =3\]

Now, \[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}={{\alpha }^{3}}{{\beta }^{3}}(\alpha +\beta )={{(\alpha \beta )}^{3}}(\alpha +\beta )\]

\[={{(3)}^{3}}\times 4=108\]

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10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

question_answer If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f(t)={{t}^{2}}-4t+3,\] then the value of \[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is: A) 104 B) 108 C) 122 D) 5

If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f(t)={{t}^{2}}-4t+3,\] then the value of \[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is:

A) 104

B) 108

C) 122

D) 5