Question

Use the discriminators to determine the number of solutions for the quadratic equation.

Y=3x^2+7x+6
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Answer 1

no real solutions

Explanation:

For a quadratic in standard form : y = ax² + bx + c : a ≠ 0

The value of the discriminant

Δ = b² - 4ac informs about the nature of the solutions

• If b² - 4ac > 0 then 2 real and distinct solutions

• If b² - 4ac = 0 then 2 real equal solutions

• If b² - 4ac < 0 then no real solutions

For y = 3x² + 7x + 6

with a = 3, b = 7, c = 6, then

b² - 4ac = 7² - (4 × 3 × 6) = 49 - 72 = - 23

Since b² - 4ac < 0 the equation has no real solutions