Answer:
Correct options are C and D
Explanation:
First we would need to expand the bracket on the left and then put the equation in standard form which is as follows:
ax² + bx + c = 0
This can be done as follows:
(2x+3)² = 10
(2x)² + 2(2x)(3) + (3)² = 10
4x² + 12x + 9 - 10 = 0
4x² + 12x - 1 = 0
By comparison, we would find that:
a = 4
b = 12
c = -1
Now, to get the roots, we would need to use the quadratic formula shown in the attached image
By substitution we would find that:
either x = [tex] \frac{-12+ \sqrt{(12)^2-4(4)(-1)} }{2(4)} = \frac{ \sqrt{10} - 3 }{2} [/tex]
or x = [tex] \frac{-12- \sqrt{(12)^2-4(4)(-1)} }{2(4)} = \frac{- \sqrt{10} - 3 }{2} [/tex]
Hope this helps :)
