Question

If x=4 is the root of x square -9x+k=0,find the value of k and hence find the other root

Answer 1

Answer:

X = 4

SO, X²-9X+K = 0...(1)

PUTTING VALUE OF X IN EQ(1)

==> (4)²-9(4)+K = 0

==> 16-36+K = 0

==> -20+K = 0

==> K = 20

SO, THE POLYNOMIAL

==> X²-9X+20

==> A = 1 , B = -9 , C= 20

BY QUADRATIC FORMULA

==> -B±√(B)²-4AC

==> -(-9) ± √(-9)²-4(1)(20)

==>  9±√81-80

==> 9±√1

==> 9±1

==> 9+1 AND 9-1

==> 10 AND 8

SO, ZEROS ARE 10 AND 8

Answer 2

Answer:

If 4 is a root of the equation x² - 9x + k = 0, then we can substitute x = 4 into the equation to find the value of k:

(4)² - 9(4) + k = 0

16 - 36 + k = 0

k = 20

Now that we know the value of k, we can use the fact that the sum of the roots of the equation is equal to -b/a and the product of the roots is equal to c/a.

x² - 9x + k = 0 is a quadratic equation with a = 1, b = -9, c = k

So, the sum of the roots is -b/a = -(-9) = 9 and the product of the roots is c/a = k/1 = 20/1 = 20

We know that one root is 4, so we can use the sum and product of the roots to find the other root.

4 + other root = 9

other root = 9 - 4 = 5

So, the other root of the equation x² - 9x + 20 = 0 is 5.