Question

Find a quadratic equation whose sum and product of the roots are -5/6 and -1.
​

Answer 1

EXPLANATION.

Quadratic equation.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -5/6.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = -1.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-5/6)x + (-1) = 0.

⇒ x² + 5x/6 - 1 = 0.

⇒ 6x² + 5x - 6 = 0.

                                                                                                                         

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Given:

• The sum of roots of a quadratic equation are -5/6
• The products of the roots are - 1

To Find:

• The quadrantic equation

Solution:

➤ Let the zeros be α and β respectively

${ \underline{ \frak{ \dag \: As \: we \: know \: that : }}}$

• The form of a quadratic equation is

➼ x² - (α+β)x + αβ

${ \underline{ \bf{ \bigstar \: According \: to \: the \: question : }}}$

Case-----(i)

➱ The sum of the zeros is - 5/6

Now,

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

${ : \implies} \sf \: \alpha + \beta = \dfrac{ - 5}{6}$

Case-----(ii)

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

${ : \implies} \sf \: \alpha \beta = - 1$

Substituting we get,

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

${ : \implies} \sf {x}^{2} - ( - \dfrac{5}{6} )x + ( - 1)$

${ : \implies} \sf {x}^{2} + \dfrac{5}{6}x - 1$

${ : \implies} \sf 6 {x}^{2} + 5x - 6$

• Hence solved.!!