Polynomials

Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$3 straight x squared minus straight x minus 4.$

Solution

We have,
3a² – x – 4 = 3x² – 4x + 3x – 4
= x(3x – 4) + 1(3x – 4)
= (x+ 1) (3x – 4)
So, the value of 3x² – a – 4 is zero, when (a + 1) = 0 or (3x – 4) = 0
i.e.,

straight x equals negative 1

straight x equals 4 over 3

Now,
Sum of zeroes =

negative 1 plus 4 over 3 equals fraction numerator negative 3 plus 4 over denominator 3 end fraction equals 1 third

fraction numerator negative left parenthesis Coefficient space of space straight x right parenthesis over denominator Coefficient space of space straight x squared end fraction

Product of zeroes =

negative 1 cross times 4 over 3 equals negative 4 over 3

space space equals space fraction numerator Constant space term over denominator Coefficient space of space straight x squared end fraction.

Some More Questions From Polynomials Chapter

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

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Polynomials

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$3 straight x squared minus straight x minus 4.$

Some More Questions From Polynomials Chapter

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
p(x) = x⁴ – 5x + 6, g(x) = 2 – x².

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
t² – 3, 2t⁴ + 3t³ – 2t²–9t – 12

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x³ – 3x + 1, x⁵ –4x³ + x² + 3x + 1.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Polynomials

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Some More Questions From Polynomials Chapter

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :p(x) = x4 – 5x + 6, g(x) = 2 – x2.

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.t2 – 3, 2t4 + 3t3 – 2t2–9t – 12

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.x3 – 3x + 1, x5 –4x3 + x2 + 3x + 1.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$3 straight x squared minus straight x minus 4.$

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
p(x) = x⁴ – 5x + 6, g(x) = 2 – x².

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
t² – 3, 2t⁴ + 3t³ – 2t²–9t – 12

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x³ – 3x + 1, x⁵ –4x³ + x² + 3x + 1.