Question

find a quadratic polynomial x square - 5and verify the relationship between the zeros and the coefficient​

Answer 1

Refer to the attachment ✔️✅

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

find a quadratic polynomial $x^5 - 5$and verify the relationship between the zeros and the coefficient

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

${\bold{\blue{\boxed{\bf{Given}}}}}$

$\sf\implies quadratic\: polynomial = x^2 - 5$

${\bold{\blue{\boxed{\bf{To\: Find }}}}}$

Relationship btw. zeros and coefficient

${\bold{\blue{\boxed{\bf{solution}}}}}$

$\sf\implies Let\:p(x) = x^2 - 5$

Zero of the polynomial is the value of x where p(x) = 0

Putting p(x)=0

$\sf\implies x^2 - 5 =0$

We can find roots using splitting the middle method

$\sf\implies x^2 - 5 =0$

$\sf\implies x^2 = 5$

$\sf\implies x =\sqrt{5}$

Therefore α = $\sqrt{5}$ and β = $-\sqrt{5}$ are the zeros of the polynomial

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Splitting the middle term method

We need to find two numbers where

Sum = 0

Product = -5

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sum of zeros = $-\sqrt{5} +\sqrt{5}$

sum of zeros = 0

product of zeros = $-\sqrt{5} \times \sqrt{5}$

product of zeros = -5

.........Hence verified

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THANK YOU❤