if 1 root of equation x²-6x+k=0 will be double than other, then k =?
Answers
Answer:
Consider the equation x
2
−6x+q=0, where a = 1, b = -6, c = q
(i) Sum of the roots m+n=
a
−b
=
1
−(−6)
∴m+n=6
(ii) Product of the roots mn=
a
c
=
1
q
∴mn=q
If one root is m then twice the root is 2m.
∴m=m and n=2m
m+n=6∴m+2m=6,3m=6∴m=
3
6
=2
We know that q=mn∴q=m(2m)=2m
2
=2(2)
2
=8∴q=8
Step-by-step explanation:
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AND FOLLOW
Given:
If the 2 roots of Quadratic equation are α and β then,
- β = 2α
To find:
Value of k = ?
Solution:
Step 1: Find out the sum of Zeros
Sum of zeros = α + β
→ Sum of Zeros = α + 2α
→ Sum of zeros = 3α
We also know that
Sum of zeros = -b ÷ a
→ 3α = -(-6) ÷ 1
→ 3α = 6
→ α = 2
Step 2: Now find out the product of zeros.
Product of zeros = α (β)
→ Product of zeros = α (2α)
→ Product of zeros = 2α²
We also know that:
Product of zeros = c ÷ a
→ 2α² = k ÷ 1
→ k = 2α²
Substitute the value of α from above.
→ k = 2(2)²
→ k = 2³
→ k = 8