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If the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of their squares, then
- a)a2+b2=c2
- b)a2+b2 = a + b
- c)ab + b2=2ac
- d)ab-b2 = 2ac
Correct answer is option 'C'. Can you explain this answer?
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If the sum of the roots of the equation ax2 + bx + c = 0 is equal to t...
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If the sum of the roots of the equation ax2 + bx + c = 0 is equal to t...
Explanation:
Given equation:
ax^2 + bx + c = 0
Sum of roots (α + β):
Sum of roots (α + β) = -b/a
Sum of squares of roots (α^2 + β^2):
Sum of squares of roots (α^2 + β^2) = (α + β)^2 - 2αβ
= (-b/a)^2 - 2c/a
= b^2/a^2 - 2c/a
Given condition:
Sum of roots = Sum of squares of roots
-b/a = b^2/a^2 - 2c/a
ab + b^2 = 2ac
Therefore, the correct answer is option C: ab + b^2 = 2ac.
Given equation:
ax^2 + bx + c = 0
Sum of roots (α + β):
Sum of roots (α + β) = -b/a
Sum of squares of roots (α^2 + β^2):
Sum of squares of roots (α^2 + β^2) = (α + β)^2 - 2αβ
= (-b/a)^2 - 2c/a
= b^2/a^2 - 2c/a
Given condition:
Sum of roots = Sum of squares of roots
-b/a = b^2/a^2 - 2c/a
ab + b^2 = 2ac
Therefore, the correct answer is option C: ab + b^2 = 2ac.
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