Question

Frame equation if roots = 4 and -12​

Answer 1

Answer:

$x^{2} + 8x -48$

Step-by-step explanation:

If α = 4, β = -12

Required polynomial =

$x^{2} - ( \alpha +\beta )x + \alpha \beta \\\\x^{2} - (4 - 12)x + (4)(-12)\\\\x^{2} - (-8)x - 48\\\\x^{2} + 8x - 48$

Answer 2

➸ Given:-

Roots of The Quadratic Equation

• 4
• -12

☣ To Find:-

• To form the Quadratic Equation.

☢ Solution:-

If $\alpha\;\&\;\beta$ are Roots of the Quadratic Equation.

$☫\;\pink{\bold{x²+(\alpha+\beta)x+\alpha\beta}}$

メ x²+(Sum of Roots)x+(Product of Roots)

${x}^{2} + (4 + ( - 12)) x + (4 \times ( - 12)) \\ {x}^{2} + (4 - 12)x + (4 \times - 12) \\ {x}^{2} + ( - 8)x + ( - 48) \\ {x}^{2} - 8x - 48$

Required Quadratic Equation

• $\Large\red{\sf{x²-8x-48 = 0}}$

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️