Class 10 Math All topics Polynomials

Quadratic polynomial having sum of it's zeros is 5 and product of it's zeros is - 14 is

(a)

$x_{2}−5x−14$

(b)

$x_{2}−10x−14$

(c)

$x_{2}−5x+14$

(d)

none of these

Correct answer: (a)

Solution: If $α$ $β$ be the zeros of the quadratic polynomial,

$(x−α )(x−β )$ is the quadratic polynomial.

$=>x_{2}−2x−βx+αβ$

$=>x_{2}−(α+β )x+αβ$

$=>x_{2}−5x+(−14)$

$=>x_{2}−5x−14$

Therefore quadratic polynomial is

$x_{2}−5x−14$

as given sum of it's zeros $5$ and product of it's zeros $−14$

then $α+β=5$ and $αβ=−14$

$(x−α )(x−β )$ is the quadratic polynomial.

$=>x_{2}−2x−βx+αβ$

$=>x_{2}−(α+β )x+αβ$

$=>x_{2}−5x+(−14)$

$=>x_{2}−5x−14$

Therefore quadratic polynomial is

$x_{2}−5x−14$

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials

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