Finding the Sum of Roots for a Quadratic Equation
The given equation is a quadratic equation in the standard form $ax^2 + bx + c = 0$.
Equation: $x^2 - 11x + 30 = 0$
By comparing the given equation with the standard form, we can identify the coefficients:
- $a = 1$
- $b = -11$
- $c = 30$
Sum of Roots Formula
For any quadratic equation $ax^2 + bx + c = 0$, the sum of its roots ($\alpha$ and $\beta$) is given by the formula:
Sum of roots = $\alpha + \beta = -\frac{b}{a}$
Calculation
Substitute the identified coefficients into the formula:
Sum of roots = $-\frac{(-11)}{1}$
Sum of roots = $\frac{11}{1}$
Sum of roots = $11$
Therefore, the sum of the roots of the equation $x^2 - 11x + 30 = 0$ is 11.
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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 + \(\frac{1}{x^3}\) .
