Question

Quadratic polynomial 6x² - 7x + 2 has zeroes as a, b, Now form a
quadratic polynomial whose zeroes are 5a and 5b

Answer 1

Answer:

6x^2-7x-3=0

Sum=α+ß

=-b/a

=-(-7)/6

=7/6

Product=αß

=c/a

=-3/6

=-1/2

Sum of new polynomial=1/α+1/ß

=(α+ß) {By substituting}

αß

=7/6+(-1/2)

7/6*(-1/2)

=7/6-3/6

7/6*(-1/2)

=4/6

-7/12

=-8/7

Product of new zeroes=1/α*1/ß

=1/(α*ß) {By substituting}

=1

-1/2

=-2

Required polynomial=k(x^2-[sum of new zeroes]x+[product of new zeroes])

=k(x^2-[-8/7]x+[-2]) {By substituting}

=k(x^2+8x/7-2)

=k(7x^2+8x-14)

7

=7x^2+8x-14(where k=7)