Question

find a quadratic polynomial whose one zero is 7 and sum of zeros is zero

Answer 1

Hii friend,

Let Alpha =7

Sum of zeros = (Alpha+Beta)

0 = 7+Beta

Beta =0-7

Beta = -7

Sum of zeros = 0

Product of zeros = Alpha × Beta = 7×-7 = -14

Therefore,

QUADRATIC POLYNOMIAL =X²-(Alpha+Beta)X + Alpha × Beta

=> X²-(0)X+(-14)

=>X²-14


HOPE IT WILL HELP YOU...... :-)

Answer 2

Answer:

$\huge{\pink{\boxed{\green{\sf{QUADRATIC=x^{2}-49}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: { \orange{given}} \\ { \pink{ \boxed{ \green{ \alpha = 7}}}} \\ { \pink{ \boxed{ \green{ \alpha + \beta = 0}}}} \\ \\ { \blue{to \: find}} \\ { \purple{ \boxed{ \red{ quadratic \: polynomial =? }}}}$

☆ According to given question:

$\to \alpha + \beta = 0 \\ \to 7 + \beta = 0 \\ \to \beta = - 7 \\ \\ for \: quadratic \\ \to( x - \alpha )(x - \beta ) \\ \to (x - 7)(x - ( - 7) ) \\ \to (x - 7)(x + 7) \\ \to {x}^{2} + 7x - 7x - 49 \\ \to {x}^{2} - 49 \\ \\ { \pink{ \boxed{ \green{ \therefore quadratic = {x}^{2} - 49 }}}}$

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