Question

write the quadratic equations whoose roots are 3 and 8​

Answer 1

Answer:

x^2-11x+24 is the answer

Answer 2

Given :

First root of the Equation = 3

Second root of the Equation = 8

To find :

The quadratic equation whose roots are given.

Solution :

Let the first root of the Equation i.e, 3 be α and

Let the other root i.e, 8 be β

Since, two roots are given, it's ba quadratic equation .

By assuming the Equation as :-

$\bf{ax^{2} + bx + c}$

Here, we know the sum product rule of the zeroes of the polynomial. i.e,

Sum :

$:\implies \bf{\alpha + \beta = -\dfrac{b}{a}}$

Where :

• b = Coeffecient of x
• a = Coeffecient of x²

Product :

$:\implies \bf{\alpha \beta = \dfrac{c}{a}}$

Where :

• c = Constant term of the Equation
• a = Coefficient of x²

Now, we get :

$:\implies \bf{x^{2} + \bigg(-\dfrac{b}{a}\bigg)x + \dfrac{c}{a}}$

By substituting the value of $\bf{-\dfrac{b}{a}}$ and $\bf{\dfrac{c}{a}}$ , we get :

$:\implies \bf{x^{2} + (\alpha + \beta)x + \alpha \beta}$

Now , by substituting the value of α and β in the equation, we get :

$:\implies \bf{x^{2} + (3 + 8)x + 3 \times 8}$

$:\implies \bf{x^{2} + 11x + 24}$

$\boxed{\therefore \bf{x^{2} + 11x + 24 = 0}}$

Hence, the quadratic equation is (x² + 11x + 24).