Question

if a and b are the zero of quadratic polynomial p(x)=3x2 - 5x -2 evaluate 1/a+1/b and a2+b2​

Answer 1

Answer:

Step-by-step explanation:

Here we will solve it by splitting the middle term method

so, 6x^2-5x-2=6x^2-3x-2x-2

Answer 2

ANSWER :–

▪︎(1/a) + (1/b) = -(5/2)

▪︎ a² + b² = 37/9

EXPLANATION :–

GIVEN :–

▪︎ A quadratic polynomial p(x) = 3x² - 5x - 2 have two roots a and b.

TO FIND :–

▪︎ (1/a) + (1/b) = ?

▪︎ a² + b² = ?

SOLUTION :–

▪︎ We know that P(x) = ax² + bx + c have two roots p and q , then –

• Sum of roots = p + q = -(b/a)

• Product of roots = p.q = (c/a)

▪︎Here –

• a = 3 , b = -5 and c = -2

• roots => p = a and q = b

• Sum of roots = a + b = -(-5/3) = 5/3

• Product of roots = a.b = -(2/3)

▪︎ Now let's find (1/a) + (1/b) –

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

= [(a + b)/ab]

= [(5/3)/(-2/3)]

= -(5/2)

=> (1/a) + (1/b) = -(5/2)

▪︎ Now let's find (a² + b²) –

= a² + b²

= (a + b)² - 2ab

= (5/3)² - 2(-2/3)

= (25/9) + (4/3)

= 37/9

=> a² + b² = 37/9

USED FORMULA :–

(1) (a + b)² = a² + b² + 2ab