Verify whether the following are zeroes of the polynomial, indicated against them.

p(x) = 3x² - 1, $straight x equals negative fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 2 over denominator square root of 3 end fraction$

Solution

p(x) = 3x² - 1, $straight x equals negative fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 2 over denominator square root of 3 end fraction$
$straight P open parentheses negative fraction numerator 1 over denominator square root of 3 end fraction close parentheses equals 3 open parentheses negative fraction numerator 1 over denominator square root of 3 end fraction close parentheses squared minus 1$
$equals 3 open parentheses 1 third close parentheses minus 1 equals 1 minus 1 equals 0 straight P open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses equals 3 open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses squared minus 1 equals 3 open parentheses 4 over 3 close parentheses minus 1 equals space 4 minus 1 equals 3 not equal to 0$
$therefore space minus fraction numerator 1 over denominator square root of 3 end fraction$ is a zero of p(x) but $fraction numerator 2 over denominator square root of 3 end fraction$ is not a zero of p(x).

Some More Questions From Coordinate Geometry Chapter

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Coordinate Geometry

Verify whether the following are zeroes of the polynomial, indicated against them.

p(x) = 3x² - 1, $straight x equals negative fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 2 over denominator square root of 3 end fraction$

Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x² - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x¹⁰+ y³ + t⁵⁰

Write the coefficients of x² in each of the following:

2 + x² + x

Write the coefficients of x² in each of the following:
2 - x² + x³

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Coordinate Geometry

Verify whether the following are zeroes of the polynomial, indicated against them.p(x) = 3x2 - 1,

Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.x10+ y3 + t50

Write the coefficients of x2 in each of the following:2 + x2 + x

Write the coefficients of x2 in each of the following:2 - x2 + x3

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Verify whether the following are zeroes of the polynomial, indicated against them.

p(x) = 3x² - 1, $straight x equals negative fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 2 over denominator square root of 3 end fraction$

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x² - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x¹⁰+ y³ + t⁵⁰

Write the coefficients of x² in each of the following:

2 + x² + x

Write the coefficients of x² in each of the following:
2 - x² + x³