Write the quadratic equation whose roots are whose roots are 5 an
d-2
Answers
Answer:
Required equation is x^2 - 3x - 10 = 0.
Step-by-step explanation:
Sum of roots = 5 + ( - 2 )
Sum of roots = 5 - 2
Sum of roots = 3
Product of roots = 5 ( - 2 )
Product of roots = - 10
Required equation : x^2 - ( sum of roots )x + product of roots = 0
= > x^2 - 3x - 10 = 0
Method 2
We know,
Any quadratic equation can also be written in this form : ( x - a )( x - b ) = 0, where a and b are the roots of the equation.
Thus, here,
= > ( x - 5 )( x + 2 ) = 0
= > x^2 + 2x^2 - 5x^2 - 10 = 0
= > x^2 - 3x - 10 = 0
Required equation is x^2 - 3x - 10 = 0.
Question :--- Write the quadratic equation whose roots are whose roots are 5 and (-2).
Formula used :---
→ if the roots of the Quadratic Equation is given as a and b , than the Quadratic Equation can be written as :--
x² - (sum of roots)*x + product of roots = 0 .
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Solution :---
→ sum of roots = 5 + (-2) = 3
→ Product of roots = 5 * (-2) = (-10)
So, Required Equation = x² - 3x -10 = 0 .
Hence, the Equation whose roots are 5 and (-2) is x²-3x-10 = 0.