Class 10 Math All topics Polynomials

If $α,β$ be the zeros of the quadratic polynomial $2−3x−x_{2}$, then $α+β=$

(a)

$2$

(b)

$9$

(c)

$1$

(d)

none of these

Correct answer: (d)

Solution: If $α$ and $β$ are the zeros of the polynomial then

$(x−α )(x−β )$ are the factors of the polynomial

Thus, $(x−α )(x−β )$ is the polynomial.

So, the polynomial $=x_{2}−αx−βx+αβ$

$=x_{2}−(α+β )x+αβ....(i)$

Now,the quadratic polynomial is

$2−3x−x_{2}=$ $x_{2}+3x−2 ....(ii)$

$(x−α )(x−β )$ are the factors of the polynomial

Thus, $(x−α )(x−β )$ is the polynomial.

So, the polynomial $=x_{2}−αx−βx+αβ$

$=x_{2}−(α+β )x+αβ....(i)$

Now,the quadratic polynomial is

$2−3x−x_{2}=$ $x_{2}+3x−2 ....(ii)$

Now, comparing equation (i) and (ii),we get,

$−(α+β )=3$

$α+β=−3$

$−(α+β )=3$

$α+β=−3$

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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