Question

if a and b are two zero of polynomial 5xsq -7x+3 find value of a sq +bsq
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Answer 1

Step-by-step explanation:

see the attachment.....

Answer 2

Answer:

a² + b² = 19/25

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros.

★ If a and b are the zeros of the quadratic polynomial Ax² + Bx + C , then ;

• Sum of zeros , (a + b) = -B/A

• Product of zeros , (ab) = C/A

Solution:

Here,

The given quadratic polynomial is ;

5x² - 7x + 3 .

On comparing with the general form of the quadratic polynomial Ax² + Bx + C ,

We have ;

A = 5

B = -7

C = 3

Also,

It is given that , a and b are the zeros of the given quadratic polynomial .

Thus,

=> Sum of zeros = -B/A

=> a + b = -(-7)/5 = 7/5

Also,

=> Product of zeros = C/A

=> ab = 3/5

Now ,

We know that ;

=> (a + b)² = a² + 2ab + b²

=> a² + b² = (a + b)² - 2ab

=> a² + b² = (7/5)² - 2•(3/5)

=> a² + b² = 49/25 - 6/5

=> a² + b² = (49 - 30)/25

=> a² + b² = 19/25

Hence,

a² + b² = 19/25