Forming New Equations MCQ Quiz - Objective Question with Answer for Forming New Equations - Download Free PDF
Last updated on Apr 11, 2025
Latest Forming New Equations MCQ Objective Questions
Forming New Equations Question 1:
If α, β are the roots of 6x2 + 13x + 7 = 0, then the equation whose roots are α2, β2 is:
Answer (Detailed Solution Below)
Forming New Equations Question 1 Detailed Solution
Given:
6x2 + 13x + 7 = 0
Concept used:
We know that a quadratic equation whose roots are α and β is given by x2 - (α + β) x + αβ = 0
Calculation:
6x2 + 13x + 7 = 0
⇒ x2 + 13x/6 + 7/6 = 0
So, (α + β) = - (13/6)
αβ = 7/6
Now,
(α + β)2 = α2 + β2 + 2αβ
⇒ 169/36 = α2 + β2 + 7/3
⇒ 169/36 - 7/3 = α2 + β2
⇒ (169 - 84)/36 = α2 + β2
⇒ 85/36 = α2 + β2
Now,
x2 - (α2 + β2)x + α2β2 = 0
⇒ x2 - 85/36x + 49/36 = 0
⇒ 36x2 - 85x + 49 = 0
∴ The required answer is 36x2 - 85x + 49 = 0.
Top Forming New Equations MCQ Objective Questions
If α, β are the roots of 6x2 + 13x + 7 = 0, then the equation whose roots are α2, β2 is:
Answer (Detailed Solution Below)
Forming New Equations Question 2 Detailed Solution
Download Solution PDFGiven:
6x2 + 13x + 7 = 0
Concept used:
We know that a quadratic equation whose roots are α and β is given by x2 - (α + β) x + αβ = 0
Calculation:
6x2 + 13x + 7 = 0
⇒ x2 + 13x/6 + 7/6 = 0
So, (α + β) = - (13/6)
αβ = 7/6
Now,
(α + β)2 = α2 + β2 + 2αβ
⇒ 169/36 = α2 + β2 + 7/3
⇒ 169/36 - 7/3 = α2 + β2
⇒ (169 - 84)/36 = α2 + β2
⇒ 85/36 = α2 + β2
Now,
x2 - (α2 + β2)x + α2β2 = 0
⇒ x2 - 85/36x + 49/36 = 0
⇒ 36x2 - 85x + 49 = 0
∴ The required answer is 36x2 - 85x + 49 = 0.
Forming New Equations Question 3:
If α, β are the roots of 6x2 + 13x + 7 = 0, then the equation whose roots are α2, β2 is:
Answer (Detailed Solution Below)
Forming New Equations Question 3 Detailed Solution
Given:
6x2 + 13x + 7 = 0
Concept used:
We know that a quadratic equation whose roots are α and β is given by x2 - (α + β) x + αβ = 0
Calculation:
6x2 + 13x + 7 = 0
⇒ x2 + 13x/6 + 7/6 = 0
So, (α + β) = - (13/6)
αβ = 7/6
Now,
(α + β)2 = α2 + β2 + 2αβ
⇒ 169/36 = α2 + β2 + 7/3
⇒ 169/36 - 7/3 = α2 + β2
⇒ (169 - 84)/36 = α2 + β2
⇒ 85/36 = α2 + β2
Now,
x2 - (α2 + β2)x + α2β2 = 0
⇒ x2 - 85/36x + 49/36 = 0
⇒ 36x2 - 85x + 49 = 0
∴ The required answer is 36x2 - 85x + 49 = 0.