Question

if alpha and beta are the zeros of quadratic polynomial 5 y square - 7 Y + 1 find the value of one upon alpha plus one upon beta​

Answer 1

Given

α and β are the zeroes of quadratic polynomial 5y² - 7y + 1

To find the value of 1/α + 1/β

We know that sum of zeroes = -b/a

product of zeroes = c/a

Comparing the given polynomial with standard quadratic polynomial ax² + bx + c, we get

a = 5

b = -7

c = 1

So,

α + β = - (-7)/5

⇒ α + β = 7/5

and, αβ = 1/5

Now,

1/α + 1/β = α/αβ + β/αβ

⇒ (α + β)/αβ

Put the values of (α + β) and αβ

⇒ $\sf\frac{\frac{7}{5}}{\frac{1}{5}}$

⇒ 7/5 × 5

⇒ 7

Hence, 1/α + 1/β = 7

Answer 2

Given that,

p(x)=5y²-7y+1

a=5, b=-7, c=1

alpha(@) +beta(€)=-b/a

=-(-7)/5=7/5

alpha ×beta=c/a

=1/5

→1/alpha+1/beta={€+@}/@€

€/@€+€/@€

@+€/@€

(7/5)/1/5

7/1

=7