Question

if a and b are the zeroes of the polynomial f(x)=2x^2-7x+3 find the value of a^2+b^2

Answer 1

Answer:

STEP BY STEP EXPLANATION GIVEN IN THE ABOVE PIC

Answer 2

Given :   a and b are the zeroes of the polynomial f(x)=2x^2-7x+3

To find : value of a^2+b^2

Solution:

Method 1 : find Zeroes :

f(x) = 2x²  - 7x  + 3

= 2x² - 6x - x + 3

= 2x(x - 3) - 1(x - 3)

= (2x - 1)(x - 3)

x = 1/2  ,  3

Zeroes are  1/2   & 3

a² + b²   = (1/2)² + 3²

= 1/4 + 9

= (1 + 36)/4

= 37/4

Method  2

Sum of zeroes  a + b  =  - (-7/2) = 7/2

Product of zeroes = ab  = 3/2

a² + b²  = ( a + b)² - 2ab

= (7/2)² - 2(3/2)

= 49/4  -  3

= (49 - 12)/4

= 37/4

a² + b² = 37/4

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