If x < 5, then the sign of the value of the expression -5x2 + 2x + 7 will be ________.
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.
Important Questions from Quadratic Equation
If 2x 2+ 5x + 1 = 0, then one of the values of \(x - \frac{1}{{2x}}\) is:
If \(a-\frac{12}{a}=1\) , where a > 0, then the value of \(a^2+\frac{16}{a^2}\) is:
If x 2 – 3x + 1 = 0, then the value of \(\frac{(x^4+\frac{1}{x^2})}{(x^2+5x+1)}\) is:
If \(\sqrt{x}{}-{1\over\sqrt{x}}=\sqrt5\) , \(x \ne 0\) , then what is the value of \((x^4+{1\over{x^2}})\over(x^2+1) \) ?
If x 2 + \(\frac{1}{x^2}\) = 18, x > 0, then find the value of x 3 + \(\frac{1}{x^3}\) .
