Question

19. Find a quadratic polynomial for which the sum and the product of zeroes

5 and3/4 respectively.
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Answer 1

Step-by-step explanation:

$\huge\underline{\underline{\sf ANSWER}} \\ \huge \: hey....$

$let \: \alpha \: and \: \beta \: be \: two \: zeros...$

$\alpha + \beta = 5 \\ \alpha \beta = \frac{3}{4}$

• Remember...

If sum and product of zeros are given quadratic equation is given as =>

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

So applying same formula in upper condition.....

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - 5x + \frac{3}{4} = 0 \\ (multiplying \: by \: 4 \: on \: both \: sides) \\ 4 {x}^{2} - 20x + 3 = 0$

Answer 2

Step-by-step explanation:

let a,b are the roots of a given quadratic equation

then,

quadratic equation=k(x2-(a+b)x+ab)=0

x2-5x+3/4=0

4x2-20x+3=0