Question

If a and ß are the zeroes
of a polynomial such
that a + B = -6 and aß =
5, then find the
polynomial. (2016 D)​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Polynomial\to x^{2}+6x+5=0}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt:\implies \alpha + \beta = - 6 \\ \\ \tt:\implies \alpha \beta = 5 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Polynomial = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) = 0 \\ \\ \tt: \implies {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0 \\ \\ \tt: \implies {x}^{2} - ( - 6)x+5= 0 \\ \\ \green{\tt: \implies {x}^{2} +6x + 5 = 0} \\ \\ \green{\tt \therefore Polynomial \to {x}^{2} + 6x + 5 = 0} \\ \\ \bold{ \blue{Some \: related \: formula}} \\ \orange{\tt \circ \: D = {b}^{2} - 4ac} \\ \\ \orange{\tt \circ \: x = \frac{ - b \pm \sqrt{D} }{2a} }$

Answer 2

CORRECT QUESTION:

If α & β are the roots of the quadratic polynomial such that α + β = - 6 & αβ = 5 , the find the quadratic polynomial

GIVEN:

• α + β = - 6
• αβ = 5

TO FIND:

• Quadratic polynomial

SOLUTION:

We know that

Quadratic polynomial = x² - ( sum of roots ) x + product of roots

→ Quadratic polynomial = x² - ( α + β )x + αβ

→ Quadratic polynomial = x² - ( - 6 )x + 5

→ Quadratic polynomial = x² + 6x + 5

Hence, required quadratic polynomial = x² + 6x + 5

MORE INFORMATION:

• Discriminant ( D ) or ∆ = b² - 4ac
• Quadratic equation formula :

x = - b±√b² - 4ac/2a

Substituting b² - 4ac = ∆

• x = - b ± √∆/2a