Given the zeroes of a cubic polynomial fx-2x3-x2-5x-2- 1-2-1-2 Verify the relation between its zeros and coefficients-

Therefore, nbsp;α nbsp;= nbsp;1/2 nbsp;β nbsp;= 1, nbsp;γ nbsp;= 2 now, nbsp; Sum of roots = nbsp;

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

Byju's Answer

Standard X

Mathematics

Relationship between Zeroes and Coefficients of a Polynomial

Given the zer...

Question

Given the zeroes of a cubic polynomial $f (x) = 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2$ Verify the relation between its zeros and coefficients.

Open in App

Solution

Therefore, $α = \frac{1}{2} β = 1, γ = - 2$
now,
Sum of roots = $fraction numerator negative left parenthesis c o e f f i c i e n t space o f space x Â² right parenthesis over denominator left parenthesis c o e f f i c i e n t space o f space x Â³ right parenthesis end fraction$
$fraction numerator negative space left parenthesis 1 right parenthesis space over denominator 2 end fraction equals space 1 half space plus space 1 space minus 2 space space L H S space equals R H S$

Products of roots = $fraction numerator negative left parenthesis space c o n s tan t space right parenthesis over denominator c o e f f i c i e n t space o f space x Â³ end fraction$
$fraction numerator negative space left parenthesis 2 right parenthesis space over denominator 2 end fraction equals space 1 half space cross times space 1 space cross times space minus 2 space minus 1 equals negative 1 L H S equals R H S$
Sum of products of two consecutive roots = $fraction numerator left parenthesis space c o e f f i c i e n t space o f space x right parenthesis over denominator c o e f f i c i e n t space o f space x Â³ end fraction$
$fraction numerator negative 5 over denominator 2 end fraction equals space 1 half space cross times space 1 space plus space 1 space cross times space left parenthesis negative 2 right parenthesis space plus space left parenthesis negative 2 right parenthesis space cross times space 1 half space space fraction numerator negative 5 over denominator 2 end fraction equals space fraction numerator negative 5 over denominator 2 end fraction$
LHS=RHS

Hence Verified

Suggest Corrections

Similar questions

Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in in each case:

(i) $f (x) = 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2$

(ii) $g (x) = x^{3} - 4 x^{2} + 5 x - 2; 2, 1, 1$

Q. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
(i)

2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2

(ii)

x^{3} - 4 x^{2} + 5 x - 2; 2, 1, 1

Q. Verify that the numbers given alongside that cubic polynomials below are its zeroes . Also verify the relationship between the zeroes and coefficient in each case.

2 x^{3} + x^{2} - 5 x + 2, (\frac{1}{2}, 1 . - 2)

Q. Verify that the numbers given along side of the cubic polynomials below are their zero.
(i)

f (x) = 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2

(ii)

g (x) = x^{3} - 4 x^{2} + 5 x - 2; 2, 1, 1

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.

Join BYJU'S Learning Program

Given the zeroes of a cubic polynomial f(x)=2x3+x2−5x+2;12,1,−2 Verify the relation between its zeros and coefficients.

Therefore, α=12β=1,γ=−2 now, Sum of roots = Products of roots = Sum of products of two consecutive roots = LHS=RHS Hence Verified

Given the zeroes of a cubic polynomial $f (x) = 2 x^{3} + x^{2} - 5 x + 2; \frac{1}{2}, 1, - 2$ Verify the relation between its zeros and coefficients.