Question

Given the sum and product of roots are -6 and 9 respectively, what is the quadratic equation?

Answer 1

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

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Sum of roots of quadratic equation is -6

$\:\:$

• Product of roots of quadratic equation is 9

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

• The quadratic equation

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the roots be $\sf \alpha \: \& \: \beta$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

➠ $\sf \alpha + \beta = -6$

$\:\:$

➠ $\sf \alpha \times \beta = 8$

$\:\:$

We know that we can find a quadratic equation whose sum and product of roots are given by -

$\:\:$

➠ $\bf x ^2 - (S)x + (P) = 0$

$\:\:$

Where,

$\:\:$

• S = Sum of roots

• P = Product of roots

$\:\:$

So , the quadratic equation will be,

$\:\:$

➜ $\sf x ^2 - (-6)x + (9) = 0$

$\:\:$

➨ x² + 6x + 9 = 0

$\:\:$

• Hence the quadratic equation whose sum and product of roots are -6 and 9 respectively is x² + 6x + 9 = 0

$\:\:$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\:\:$

ᗩᗪᗪITIOᑎᗩᒪ IᑎᖴOᖇᗰᗩTIOᑎ

$\:\:$

• General form of quadratic equation is ax² + bx + c = 0 [ a ≠ 0 ]

• Sum of its roots = $\sf \dfrac { -b } { a }$

• Product of its roots = $\sf \dfrac { c} { a }$

• The degree of a quadratic equation is 2

• Quadratic equation can be solved by following ways -

$\:\:$

✰ Factoring

✰ Completing the Square

✰ Quadratic Formula

✰ Graphing

$\:\:$

═════════════════════════

Answer 2

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

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Sum of roots of quadratic equation is -6

$\:\:$

• Product of roots of quadratic equation is 9

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

• The quadratic equation

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the roots be $\sf \alpha \: \& \: \beta$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

➠ $\sf \alpha + \beta = -6$

$\:\:$

➠ $\sf \alpha \times \beta = 8$

$\:\:$

• We know that we can find a quadratic equation whose sum and product of roots are given by -

$\:\:$

➠ $\bf x ^2 - (S)x + (P) = 0$

$\:\:$

Where,

$\:\:$

S = Sum of roots

P = Product of roots

$\:\:$

• So , the quadratic equation will be,

$\:\:$

➜ $\sf x ^2 - (-6)x + (9) = 0$

$\:\:$

➨ x² + 6x + 9 = 0

$\:\:$

• Hence the quadratic equation whose sum and product of roots are -6 and 9 respectively is x² + 6x + 9 = 0

$\:\:$

═════════════════════════