Question

A quadratic has roots of -3 and -2. What is its equation?

Answer 1

Answer:

x^2 +5x +6=0

Step-by-step explanation:

x^2 -( sum of roots)x + (product of roots)

= x^2-(-5x)+6=0

or, x^2 +5x+6=0

Answer 2

Solution:-

Let the be α & β are the zero of Quadratic Equation.

Now ,

Using Formula of Quadratic Equations

→ x² - (Sum of Roots )x + (Product of Roots)

Substitute the value we get

→ x² - (α + β)x + αβ

→ x² - (-3 -5)x + (-2)(-3) = 0

→ x² -(-5)x + 6 = 0

→ x² +5x + 6 = 0

Therefore , the Quadratic Equation should be x² +5x +6 .

Additional Information!!

Some More identities!!

• (a + b)² = a² + b² +2ab

• ( a - b )² = a² + b² -2ab

• ( a² - b² ) = ( a - b ) ( a + b )

• ( a +b +c)² = (a² + b² + c²) + 2(ab + bc +ca)

• (a + b)³ = a³ + b³ + 3ab(a+b)

• (a-b)³ = a³ - b³ -3ab(a-b)

• ( a³ + b³) = (a+b) (a²-ab +b²)

• (a³ - b³) = (a -b) (a² + ab + b²)