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JEE • MATHEMATICS • THEORY OF EQUATION

Theory of equation practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 61-63 of 63 questions

61 Easy

61 of 63

Application +4 | -1

The solution of the equation

2{x^3} - {x^2} - 22x - 24 = 0

when two of the roots in the ration

3:4

, is

View answer and explanation

Correct option: B

- \frac{3}{2},\; - 2,\;4

Option B (

- \frac{3}{2},\; - 2,\;4

) is correct because it satisfies the given equation and the ratio of two of its roots is 3:4.

62 Easy

62 of 63

Application +4 | -1

Let

\mathrm{p}(\mathrm{x})

be a quadratic polynomial such that

\mathrm{p}(0)=1

. If

\mathrm{p}(\mathrm{x})

leaves remainder 4 when divided by

\mathrm{x}-1

and it leaves remainder 6 when divided by

x+1

; then :

View answer and explanation

Correct option: C

\mathrm{p}(-2)=19

Option C (

\mathrm{p}(-2)=19

) is correct because when the quadratic polynomial p(x) is determined based on the given conditions, p(-2) evaluates to 19.

63 Easy

63 of 63

Application +4 | -1

\alpha ,\;\beta \;

and

\gamma

are the roots of the equation

{x^3} - 8x + 8 = 0

, then

\sum {\alpha ^2}\;\mathrm{and}\;\,\sum \frac{1}{{\alpha \beta }}\;

are respectively

View answer and explanation

Correct option: D

16 and 0

Option D (16 and 0) is correct because it is found by using Vieta's formulas and the given equation to calculate the sum of squares and the sum of reciprocals of the product of roots.

Revision notes and key takeaways

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