Question

If (a-b) and (a+b) are zeroes of the polynomial f(x)=2x^3-6x^2+5x-7 find the value of a​

Answer 1

The given Polynomial has $<b>3</b>$ zeroes.




$<b>Step I :</b>$ $<u>Assumption</u>$

Let $<b>( a - b ), a & ( a + b ) </b>$ be the zeroes.




$<b>Step II :</b>$ $<u>Determine a, b, c and d.</u>$

f ( x ) = 2x³ - 6x² + 5x - 7

On comparing with ax³ + bx² + cx + d, we get

a = 2, b = - 6, c = 5, d = - 7




$<b>Step III :</b>$ $<u>Determine the value of a by sum of zeroes.</u>$

$<u>Sum of zeroes = - b / a</u>$

Also, Sum of zeroes = ( a - b ) + a + ( a + b )

$\therefore$

- b / a = ( a + b ) + a + ( a - b )

- ( - 6 ) / 2 = 3a

3 = 3a

a = 3 / 3 = 1




Hence, $<u>the value of a is</u>$ $<u><I><b> 1.</b></u></I>$