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How many real solutions does a quadratic equation have if its discriminant is zero

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User Itiic
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2 Answers

4 votes
0 , 1 , or 2 solutions hope this helps :D
answered
User James McCormack
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8.2k points
3 votes
If the discriminant of a quadratic is 0 then it means that the quadratic has two non-distinct roots or simply 1 real root. Thus the answer would be OPTION B



So an example would be 9x² + 12x + 4 = 0 in the form ax² + bx + c

the discriminant would be b² - 4ac = (12²) - 4(9)(4)
= 0

Now to solve to prove true
9x² + 12x + 4 = 9x² + 6x + 6x + 4 = 0

⇒ 9x² + 6x + 6x + 4 = 0
by factorising
3x(3x + 2) + 2(3x + 2)= 0

9x² + 6x + 6x + 4 = (3x + 2)²
which means it only has one root at x= 2/3
answered
User Sean McKenzie
by
8.0k points

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