If alpha and beta are the zeros of the polynomial 3x square - 4x - 7 . Then form a quadratic polynomial whose zeros are 1/alpha and 1/ beta
Answers
Step-by-step explanation:
There ya go. ans in pic. hope it helps
Step-by-step explanation:
Given that α and β are the zeroes of the polynomial 3x^2 - 4x - 73x
2
−4x−7 then we have to find a quadratic equation whose zeroes are
\frac{1}{\alpha}\text{ and }\frac{1}{\beta}
α
1
and
β
1
3x^2 - 4x - 73x
2
−4x−7
3x^2-7x+3x-73x
2
−7x+3x−7
x(3x-7)+(3x-7)x(3x−7)+(3x−7)
(x+1)(3x-7)(x+1)(3x−7)
\text{The zeroes of polynomial }\alpha\text{ and }\beta\text{ are } -1, \frac{7}{3}The zeroes of polynomial α and β are −1,
3
7
\frac{1}{\alpha}=\frac{1}{-1}=-1
α
1
=
−1
1
=−1
\frac{1}{\beta}=\frac{1}{\frac{7}{3}}=\frac{3}{7}
β
1
=
3
7
1
=
7
3
∴ The quadratic equation is
(x+1)(x-\frac{3}{7})=0(x+1)(x−
7
3
)=0
x^2-\frac{3x}{7}-x+\frac{3}{7}=0x
2
−
7
3x
−x+
7
3
=0
x^2-\frac{10}{7}x+\frac{3}{7}=0x
2
−
7
10
x+
7
3
=0