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lapo4ka [179]
3 years ago
11

One of the solutions to the equation 5x^2+bx+12=0 is -4/5

Mathematics
1 answer:
Rzqust [24]3 years ago
4 0

Answer:

x = -3

Step-by-step explanation:

Given equation:

5x^2+bx+12=0

This equation has known solution -\frac{4}{5}, this means that

5\cdot \left(-\dfrac{4}{5}\right)^2+b\cdot \left(-\dfrac{4}{5}\right)+12=0

Solve it for b:

5\cdot \dfrac{16}{25}-\dfrac{4b}{5}+12=0\\ \\\dfrac{16}{5}-\dfrac{4b}{5}+12=0\\ \\16-4b+12\cdot 5=0\ \ [\text{Multiplied by 5}]\\ \\16-4b+60=0\\ \\-4b=-12-60\\ \\-4b=-76\\ \\4b=76\\ \\b=19

Therefore, the equation is

5x^2+19x+12=0

Solve it using quadratic formula:

D=b^2-4ac=19^2-4\cdot 5\cdot 12=361-240=121\\ \\\sqrt{d}=\sqrt{121}=11\\ \\x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}=\dfrac{-19\pm 11}{2\cdot 5}=-3,\ -\dfrac{4}{5}

The other solution is x = -3

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