Find the zeros of the cubic polynomial p-x- - x3 - 2x2 ndash- 3x- Also verify the relationship between the zeros and coefficients of p-x- -8203-

Hi, #160;fx= #160;x3+2x2 3xcomparing #160;it #160;with #160;ax3+bx2+cx+da #160;= #160;1 #160;, #160;b= #160;2 #160;, #160;c #160;= # ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Zeroes of a Polynomial

Find the zero...

Question

Find the zeros of the cubic polynomial p(x) = x3 + 2x2 – 3x. Also verify the relationship between the zeros and coefficients of p(x).

Open in App

Solution

$Hi, f (x) = x^{3} + 2 x^{2} - 3 x comparing it with {ax}^{3} + {bx}^{2} + cx + d a = 1, b = 2, c = - 3, d = 0 = x (x^{2} + 2 x - 3) = x (x^{2} - x + 3 x - 3) = x (x (x - 1) + 3 (x - 1)) = x (x - 1) (x + 3) so zeroes are x = 0, 1, - 3 so sum of roots from equation = \frac{- b}{a} = - 2 from the roots calculated, sum = 0 + 1 - 3 = - 2 sum of roots taken two at a time, from equation = \frac{c}{a} = - 3 from the roots calculated, sum of roots taken two at a time = 0 \times 1 + 1 \times (- 3) + (- 3) \times 0 = - 3 and product of roots from equation = \frac{- d}{a} = 0 from the roots calculated, product = 0 \times 1 \times (- 3) = 0$

Suggest Corrections

Similar questions

Verify that 3, -2, 1 are the zeros of the cubic polynomial $p (x) = x^{3} - 2 x^{2} - 5 x + 6$ and verify the relation betweeen its zeros and coefficients.

Q. Verity that 3, −2, 1 are the zeros of the cubic polynomial p(x) = x³ − 2x² − 5x + 6 and verify the relation between its zeros and coefficients.

Find the zeroes of the polynomial $p (x) = 2 x^{2} - 5 x - 12$ and verify the relationship between its zeroes and coefficients.

Q. If

α, β, γ

are the zeros of the cubic polynomial

p (x) = x^{3} + 2 x^{2} - 3 x

then

α \cdot β \cdot γ =

_____

Q. Prove that

4

and

1

are the zeros of the quadratic polynomial

p (x) = x^{2} - 5 x + 4

. Also verify the relationship between the zeros and the coefficients of

p (x)

Join BYJU'S Learning Program

Find the zeros of the cubic polynomial p(x) = x3 + 2x2 – 3x. Also verify the relationship between the zeros and coefficients of p(x).​

Find the zeros of the cubic polynomial p(x) = x3 + 2x2 – 3x. Also verify the relationship between the zeros and coefficients of p(x).