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What is the discriminant of the quadratic equation 4x^(2)+3x-6=0 ? -105 87 105 -87

What is the discriminant of the quadratic equation 4x2+3x−6=0 4 x^{2}+3 x-6=0 ?\newline−105 -105 \newline8787\newline105105\newline−87 -87

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Full solution

Q. What is the discriminant of the quadratic equation 4x2+3x−6=0 4 x^{2}+3 x-6=0 ?\newline−105 -105 \newline8787\newline105105\newline−87 -87
  1. Identify Coefficients: The discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by the formula D=b2−4acD = b^2 - 4ac. We need to identify the coefficients aa, bb, and cc from the given equation 4x2+3x−6=04x^2 + 3x - 6 = 0.
  2. Substitute into Formula: The coefficients are a=4a = 4, b=3b = 3, and c=−6c = -6. Now we will substitute these values into the discriminant formula D=b2−4acD = b^2 - 4ac.
  3. Calculate Discriminant: Substituting the values, we get D=(3)2−4(4)(−6)=9−(−96)=9+96D = (3)^2 - 4(4)(-6) = 9 - (-96) = 9 + 96.
  4. Find Final Value: Calculating the sum, we find that D=9+96=105D = 9 + 96 = 105.

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