1.) Find the value of p, for which one of the roots of the equation 
is 6 times the other
2.) if α & β are the roots of 
and 
find the value of a.
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Step by step explanation ✅
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Answers
Answer:
1) p = 3
2) a = –24
Step-by-step explanation:
TO KNOW :
For a quadratic equation of the form ax² + bx + c = 0 ;
sum of roots = –(x coefficient)/x² coefficient = –b/a
product of roots = constant/x² coefficient = c/a
1) Given :
One of the roots of the equation px²-14x+8 = 0 is 6 times the other
To find :
the value of p
Solution :
Let one root be a
then the other root = 6a
For the given quadratic equation,
x² coefficient = p
x coefficient = –14
constant = 8
Sum of roots :
a + 6a = –(–14)/p
7a = 14/p
a = 14/7p
a = 2/p
Product of roots :
a × 6a = 8/p
6a² = 8/p
6(2/p)² = 8/p
6 × (4/p²) = 8/p
24/p² = 8/p
24/p = 8
p = 24/8
p = 3
The value of p is 3
_______________________
2) Given :
- α & β are the roots of x²+5x+a = 0 and
- 2α+5β = -1
To find :
the value of a
Solution :
For the given quadratic equation,
x² coefficient = 1
x coefficient = 5
constant = a
Sum of roots :
α + β = –5/1
α + β = –5
Product of roots :
αβ = a
2α + 5β = –1
2α + 2β + 3β = –1
2(α + β) + 3β = –1
2(–5) + 3β = –1
–10 + 3β = –1
3β = –1 + 10
3β = 9
β = 9/3
β = 3
α + β = –5
α + 3 = –5
α = –5 – 3
α = –8
αβ = a
(–8)(3) = a
a = –24
The value of a is –24
1. Hence the Answer is p = 3.
2. Answer value of a = -24.
Step-by-step explanation:
Note : Explanation is written in the attachment.
