Question
If x < 5, then the sign of the value of the expression -5x2 + 2x + 7 will be ________.
The correct answer is
Can't be said
Given:
x < 5
− 5x2 + 2x + 7
Concept Used:
x2 – (sum of roots)x + product of roots = 0
Calculation:
− 5x2 + 2x + 7 = 0
⇒ −5x2 + 7x − 5x + 7 = 0
⇒ x(− 5x + 7) + (− 5x + 7) = 0
⇒ (x + 1)(7 − 5x) = 0
⇒ x = −1 and x = 7/5
Both roots are less than 5.
∴ We cannot determine the sign of the expression.
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