Question

If the sum of roots of an equation is 1 and their product is-6. Write the equation.

Answer 1

GIVEN :–

• Sum of roots = 1

• Product of roots = -6

TO FIND :–

• Quadratic equation = ?

SOLUTION :–

• Let the roots of quadratic equation are α and β.

➪ α + β = 1

➪ β = 1 - α __________eq.(1)

& αβ = -6

• So that –

⇒ α(1 - α) = -6 [ Using eq.(1) ]

⇒ α - α² = -6

⇒ α² - α - 6 = 0

⇒ α² - 3α + 2α - 6 = 0

⇒ α(α - 3) + 2(α - 3) = 0

⇒ (α + 2)(α - 3) = 0

⇒ α = -2 , 3

• Similarly –

⇒ β = 1 - (-2) , 1 - 3

⇒ β = 1 + 2 , 1 - 3

⇒ β = 3 , -2

• So the quadratic equation is –

⇨ (x - α)(x - β) = 0

⇨ [x - (-2)](x - 3) = 0

⇨ (x + 2)(x - 3) = 0

⇨ x² + 2x - 3x - 6 = 0

⇨ x² - x - 6 = 0

•Hence , The quadratic equation is x² - x - 6 = 0.

Answer 2

Step-by-step explanation:

Question :-

If the sum of roots of an equation is 1 and their product is-6. Write the equation.

Answer :-

Given :

• Sum of roots = 1
• Product of roots = -6

Let's take the roots be x and y

To find :

• Quadratic equation

Solution :

According to question,

• x + y = 1
• xy = -6

We know the quadratic equations formula that is,

$➨ \: \: \: \: \: {\bold{\sf{\fbox{x² \: - \: (sum of roots)x+(products of roots) \: = \: 0}}}}$

Substituting the values,

${\bold{\sf{⟼ \: \: \: \: \: \: x² \: - \: x \: + \: (-6)}}}$

${\bold{\sf{⟼ \: \: \: \: \: \: x² \: - \: x \: - \: 6}}}$

Hence the quadratic equation that form is,

$➤ \: \: \: \: \: \: \: \: \: \: \: {\bold{\bf{\fbox{\pink{x² \: - \: x \: - \: 6}}}}}$