Solving the Number Equation
Let the unknown number be represented by the variable $x$.
Formulating the Algebraic Equation
The problem states that squaring the number ($x^2$) and subtracting twice the number ($- 2x$) results in 80 ($= 80$). This forms the equation:
$x^2 - 2x = 80$
Solving the Quadratic Equation
To find the value of $x$, we rearrange the equation into the standard quadratic form ($ax^2 + bx + c = 0$):
$x^2 - 2x - 80 = 0$
We can solve this quadratic equation by factoring. We look for two numbers that multiply to $-80$ and add to $-2$. These numbers are $-10$ and $+8$.
Factoring the equation gives:
$(x - 10)(x + 8) = 0$
This equation yields two possible solutions for $x$:
- $x - 10 = 0 \implies x = 10$
- $x + 8 = 0 \implies x = -8$
Identifying the Number from Options
The possible values for the number are 10 and -8. Reviewing the provided options (10, 15, 20, 25), the value 10 is present.
Thus, the number satisfying the condition is 10.
Important Questions from Quadratic Equation
For what values of k, the roots of 9x 2 + 8kx + 16 = 0 are real and equal?
- If \(\rm \left( \frac{x}{x+1} \right)^2 -5 \left( \frac{x}{x+1} \right) +6=0 \) , then the value of \(\rm \left( 1+\frac{1}{x} \right) \) is equal to :
The nature of the roots of the equation 4x 2 - 2x - 3 = 0.
If the roots of the equation (q – r)x 2+ (r – p)x + (p – q) = 0 are equal, then which of the following is true?
Number of real roots of the quadratic equation 3x 2+ 4x + 25 = 0 is
