Question

7. If a and b are the roots of x2 -3x -1 = 0, then form a quadratic equation whose roots are 1 /a2 and 1/b2 .

Answer 1

a and b are the roots of x² - 3x - 1 = 0
sum of roots = - Coefficient of x/coefficient of x²
a + b = -(-3)/1 = 3
product of roots = constant/coefficient of x²
ab = (-1)/1 = -1

now, we have to find out equation whose roots are 1/a² and 1/b²
sum of roots = 1/a² + 1/b² = (a² + b²)/(ab)²
= [(a + b)² - 2ab]/(ab)²
=[3² - 2(-1)]/(-1)²
= 11
product of roots = 1/a².1/b² = 1/(ab)² = 1/(-1)² = 1
so, equation is x² - (sum of roots)x + product of roots = 0
x² - 11x + 1 = 0

Answer 2

HELLO DEAR,

given, a and b are the roots of the equation x² - 3x - 1 = 0

now, a + b = -(coff. Of x)/(coffi.of x²)
a + b = -(-3)/1 = 3

a*b = (constant term)/(coff.of x²)
a*b = -1/1 = -1

now, we have to find 1/a² + 1/b²

(1/a² + 1/b²) = (a² + b²)/(ab)²
(1/a² + 1/b²) = [(a + b)² - 2ab)]/(-1)²
(1/a² + 1/b²) = [9 - 2(-1)]/1
(1/a² + 1/b²) = 11

And, 1/a² * 1/b² = 1/(ab)² = 1/(-1)² = 1

we know the formula for quadratic equations,
x² - (1/a² + 1/b²)x + (1/a² * 1/b²) = 0
x² - 11x + 1 = 0
hence,the required equation is x² - 11x + 1 = 0

I HOPE ITS HELP YOU DEAR,
THANKS