Question

10.
If a and B are zeroes of the polynomial 5x2 + 5x + 1, then find the value of (i) a² + B2 , (ii)
a-1 + B-1​

Answer 1

Answer:

1/ o

2/ -2

Explanation:

0 multiplied by any no. will become 0

0-(-1)=-1

-1+(-1)=-2

Answer 2

Explanation:

i) 3/5

ii) -5

\rule{200}1

Explanation

Given,

zeroes of polynomial p(x) = 5x² + 5x + 1 are a, b

To find,

the value of a² + b² and 1/a + 1/b

We know that sum of zeroes = \sf -\frac{coefficient\ of\ x}{coefficient\ of\ x^2}−

coefficient of x

2

coefficient of x

So, we get a + b = -5/5 = -1

And, product of zeroes = \sf \frac{constant}{coefficient\ of\ x^2}

coefficient of x

2

constant

→ ab = 1/5

Now,

i) a² + b² = (a + b)² - 2ab

→ a² + b² = (-1)² - 2/5

→ a² + b² = 1 - 2/5

→ a² + b² = 3/5

ii) 1/a + 1/b = (a + b)/ab

→ \sf\frac{-1}{\frac{1}{5}}

5

1

−1

→ 1/a + 1/b = -5