Question

Write the quadratic equation whose roots are whose roots are 5 an
d-2

Answer 1

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.

Answer 2

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 .

__________________

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.