The difference between the roots of the quadratic equation x^2 - kx + 21 = 0 is 4. Find the values of k.?

Question

plz show da working.... TQ

Answer 1

k=±11

21 is the product of 7 and 3 or -7 and -3. Since k is the sum of the roots, adding the solutions for each possible set of answers will get you k=11 or k=-11

Answer 2

1. k=+10

2. (x-3)*(x-7)=x^2-10x+21

3+7=10

3*7=21

Answer 3

Nobody who's answered so far is reading the question right....  Note the directions say "the difference between the roots is 4".

Root #1 = a

Root #2 = a + 4

(x - root 1)(x - root 2) = given equation

(x - a)[x - (a + 4)] = x^2 - kx + 21

(x - a)(x - a - 4) = x^2 - kx + 21

x^2 - ax - 4x - ax - a^2 + 4a = x^2 - kx + 21

x^2 - 2ax - 4x - a^2 + 4a = x^2 - kx + 21

x^2 - (2a + 4)x + (4a - a^2) = x^2 - kx + 21

so...

2a + 4 = k

and

4a - a^2 = 21

Solve the second one for a....

-a^2 + 4a - 21 = 0

a^2 - 4a + 21 = 0

(a - 7)(a + 3) = 0

a = 7, -3

So, a = 7 or a = -3

Now, use the other equation to find k.

a = 7

2a + 4 = k

17 + 4 = k

21 = k

a = -3

2a + 4 = k

-6 + 4 = k

-2 = k

So, k = 21 or -2

Answer 4

-7 and -3

Answer 5

Difference of roots of a quadratic equation is

abs (sqrt(Discriminant))/coefficient of x^2

here Discriminant or D = k^2 - 84 and coefficient of x^2 is 1.

now abs(sqrt(k^2 - 84)) = 4

=> k^2 - 84 = 16  

=> k = 10 or k = -10

Therefore two values of k are possible.