Question

Short Answer Type
9. If a and B are the zeroes of the quadratic
polynomial 3.x2 - 5x – 2, find the value of a2 + B2.​

Answer 1

Step-by-step explanation:

Given :-

a and B are the zeroes of the quadratic

polynomial 3x² - 5x – 2.

To find :-

Find the value of a² + B²?

Solution :-

Given Quadratic Polynomial is 3x²-5x-2

On Comparing this with the standard quadratic Polynomial ax²+bx+c

We get

a = 3

b = -5

c = -2

Given zeroes of p(x) are a and B

We know that

Sum of the Zeroes = -b/a

=> a + B = -(-5)/3

a + B = 5/3 -----------(1)

Product of the zeroes = c/a

=> a × B = -2/3 --------(2)

We know that

(a+b)² = a²+b²+2ab

=> a²+b² = (a+b)²-2ab

On applying this

a²+B² = (a+B)²-2aB

From (1)&(2)

=> a²+B² = (5/3)²-2(-2/3)

=> a²+B² = (25/9)-(-2×2)/3

=>a²+B² = (25/9)-(-4/3)

=> a²+B² = (25/9)+(4/3)

LCM of 3 and 9 = 9

=> a²+B² = (25+12)/9

=>a²+B² = 37/9

Answer:-

The value of a²+B² for the given problem is 37/9

Used formulae:-

• The standard quadratic polynomial is ax²+bx+c

• Sum of the zeroes = -b/a

• Product of the zeroes = c/a

• (a+b)²=a²+2ab+b²