find a quadratic polynomial each with given numbers as the sum and product of its zeroes respectively
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find a quadratic polynomial each with given numbers as the sum and product of its zeroes respectively
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Answer:
3x^2-3√2x+1
Step-by-step explanation:
Alpha +beta=-b/a
alpha×beta = C/a
Verified answer
ii ) sum zeroes = √2
[tex] \frac{ - b}{a} = \frac{ \sqrt{2} }{1} [/tex]
[tex]\frac{ b}{a} = \frac{ - \sqrt{2} \times 3}{1 \times 3} [/tex]
[tex]\frac{ b}{a} = \frac{-3 \sqrt{2} }{3} [/tex]
product of zeroes =1/3
[tex] \frac{c}{a} = \frac{1}{3} [/tex]
Therefore a =3 , b =- 3√2 , c = 1
Quadratic polynomial is ax²+bx+c
= 3x²- 3√2x +1
v )
sum of zeroes = - 1/4
[tex] \frac{ - b}{a} = \frac{ - 1}{4} [/tex]
[tex] \frac{ b}{a} = \frac{ 1}{4} [/tex]
product of zeroes = 1/4
[tex] \frac{ c}{a} = \frac{ 1}{4} [/tex]
Therefore a =4 , b = 1 , c = 1
Quadratic polynomial is ax²+bx+c
= 4x²+1x +1
or 4x²+ x +1