Question

plz help.............. ....​

Answer 1

$\large{\underline{\underline{\red{\bf{Answer:}}}}}$

The polynomial is k[x²+5x+3].

$\rule{200}4$

$\large{\underline{\underline{\red{\bf{Step\:by\:step\: explanation:}}}}}$

${\underline{\underline{\purple{\bf{Given:}}}}}$

Sum of zeroes of a polynomial is -5.

Product of zeroes is 3.

${\underline{\underline{\purple{\bf{To\: Find:}}}}}$

The quadratic polynomial.

${\underline{\underline{\purple{\bf{Answer:}}}}}$

Given that the sum of zeroes is (-5) and the product of the zeroes is 3.

So , here's a formula to find the quadratic polynomial when the sum and product of zeroes is given.

$\large{\underline{\boxed{\purple{\bf{\leadsto p(x)=k[x^2-(\alpha+\beta)x +\alpha\beta]}}}}}$

where ,

Alpha and beta are zeroes.

p(x) is polynomial.

k is a constant.

Using this formula ,

$\sf{\implies p(x) = k[x^2 -(-5)x + 3 ]}$

$\orange{\sf{\implies p(x) = k[ x^2 +5x +3]}}$

${\underline{\underline{\pink{\bf{\longmapsto Hence \:the\: required\: polynomial\:is\:k[x^2+5x+3]}}}}}$

Answer 2

$\large{\underline{\underline{\red{\bf{Answer:}}}}}$

The polynomial is k[x²+5x+3].

$\rule{200}4$

$\large{\underline{\underline{\red{\bf{Step\:by\:step\: explanation:}}}}}$

${\underline{\underline{\purple{\bf{Given:}}}}}$

Sum of zeroes of a polynomial is -5.

Product of zeroes is 3.

${\underline{\underline{\purple{\bf{To\: Find:}}}}}$

The quadratic polynomial.

${\underline{\underline{\purple{\bf{Answer:}}}}}$

Given that the sum of zeroes is (-5) and the product of the zeroes is 3.

So , here's a formula to find the quadratic polynomial when the sum and product of zeroes is given.

$\large{\underline{\boxed{\purple{\bf{\leadsto p(x)=k[x^2-(\alpha+\beta)x +\alpha\beta]}}}}}$

where ,

Alpha and beta are zeroes.

p(x) is polynomial.

k is a constant.

Using this formula ,

$\sf{\implies p(x) = k[x^2 -(-5)x + 3 ]}$

$\orange{\sf{\implies p(x) = k[ x^2 +5x +3]}}$

${\underline{\underline{\pink{\bf{\longmapsto Hence \:the\: required\: polynomial\:is\:k[x^2+5x+3]}}}}}$