If the roots of a quadratic equation: Ax^{2}+Bx+C=0 are x=5 and x=\frac{4}{3}, then what is the equation?

amanf

amanf

Answered question

2021-04-26

If the roots of a quadratic equation: Ax2+Bx+C=0 are x=5andx=43, then what is the equation?

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-04-28Added 99 answers

Step 1
Consider the given quadratic equation:
Ax2+Bx+C=0
Root of the above equation is x=5 and x=43
Here, the objective is to find the equation
Step 2
Re-write the given quadratic equation after dividing both sides by A
x2+BAx+CA=0...(1)
Since
The sum of roots of quadratic equation =BA
5+43=BA
5×33+43=BA
153+43=BA
193=BA
BA=193
The product of roots of quadratic equation =CA
5×43=CA
203=CA
CA=203
Use equation (1)
x2+BAx+CA=0
Substitute BA=193andCA=203
x2193x+203=0
3x219x+20=0
Hence, the required quadratic equation is 3x219x+20=0

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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