Question

class 10 polynomial 3 x square - 8 x + 2 k + 1 is 7 times the other find value of k

Answer 1

3x²-8x+2k+1 = p(x) where a= 3, b= -8 and c= 2k+1
Let p and q be the roots of this polynomial.
Then according to the question
q=7p
As it is given one root is 7 times the other.
Now we know
sum of the roots= -b/a
Putting the values we get
p+ q= -(-8)/3
p+7p = 8/3
8p= 8/3
p= (8/3)*(1/8)
p=1/3........(1)


Now, we know
multiplication of the roots = c/a
Putting the values we get

p*q= (2k+1)/3

p*7p= (2k+1)/3

7p²= (2k+1)/3

7(1/3)²=(2k+1)/3.........from(1)
(7/9)=(2k+1)/3

21= 9(2k+1)

21=18k+9

21-9= 18k
12= 18k
k = 12/18

k= 2/3
Hope this helps you