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Answer

e) root 24

Explanation

x^2 + px + 6 = 0 has equal roots.

This means it has 1 root which is repeated.

Therefore when the values are inserted in the quadratic formula you should obtain one root.

This can only be done when the discriminant b^2 - 4ac = 0.

x = -b + or - root 0 (discriminant) / 2a

Therefore x = -b/2a

Where ax^2 + bx + c is the quadratic.

Insert a= 1 and b = p

-p/2 is the root

Therefore x = -p/2 when y = 0 (as the root is an x-axis intercept.

Substitute x = -p/2 in equation in question

(-P/2)^2 + -p^2/2 + 6 = 0

p^2/4 - p^2/2 = -6

Subtract fractions

- p^2/4 = -6

-p^2 = -24

p^2 = 24

p = square root 24

√24

Option C is the correct option.

Please see the attached picture for full solution.

Hope it helps ...

Good luck on your assignment...