Question

find the
quadratic polynomial whose
Sum and product the zeros are
21 /8 and 5/16 and respectively​

Answer 1

Given:

• Sum of roots ( α + β ) = 21/8
• Product of roots ( αβ ) = 5/16

To Find:

• The quadratic polynomial.

Solution:

As we know that,

$\implies$ Quadratic polynomial = x² - ( α + β )x + αβ = 0

[ Putting values ]

$\implies$ Quadratic polynomial = x² - 21/8x + 5/16 = 0

Hence,

• The quadratic polynomial is x² - 21/8x + 5/16 = 0.

Answer 2

Step-by-step explanation:

• Sum of its zeroes = $\sf \alpha +\beta =\dfrac{21}{8}$

• Product of its zeroes= $\sf \alpha \beta = \dfrac{5}{16}$

Formula to form a quadratic polynomial:

$= > \sf p(x)=k \bigg \lgroup x^{2} -(\alpha +\beta )x+\alpha \beta \bigg \rgroup$

$=> \sf p(x)= k \bigg\lgroup x^{2} - \bigg(\dfrac{21}{8} \bigg )x+\dfrac{5}{16} \bigg \rgroup$

$=> \sf p(x)= 16 \bigg \lgroup x^{2} -\bigg(\dfrac{21}{8} \bigg)x+\dfrac{5}{16} \bigg \rgroup$

$=> \sf p(x)= \bigg\lgroup 16x^{2} -42x+5\bigg\rgroup$

• The quadratic polyniomial is :

$\: \: \: \: \: \: \: \: \: \: \: \bullet \: \: \boxed{\textsf{ \textbf{16x ^{2} - 42x + 5}} }$