To determine the nature of the zeros of the quadratic equation \(x^2 - 7x + 6 = 0\), we need to evaluate the discriminant. The discriminant, \(\Delta\), for a quadratic equation of the form \(ax^2 + bx + c = 0\) is given by:
\(\Delta = b^2 - 4ac\)
For our equation, \(a = 1\), \(b = -7\), and \(c = 6\). Substituting these values in, we get:
\(\Delta = (-7)^2 - 4 \times 1 \times 6 = 49 - 24 = 25\)
The discriminant is 25, which is greater than zero. This indicates that the zeros of the equation are two distinct real numbers.
Thus, the nature of the zeros of the equation is Real and unequal, confirming that this is the correct choice. Here's a breakdown of the options given:
- Real and equal: This would be the case if \(\Delta = 0\).
- One is real and one imaginary: This would occur if \(\Delta < 0\).
- Imaginary: This would also imply \(\Delta < 0\).
- Real and unequal: This condition is met when \(\Delta > 0\), which matches our case.
Therefore, the correct answer is Real and unequal.
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If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct?
If the roots of the equation x 2+ px + q = 0 are tan 19° and tan 26°, then which one of the following is correct?
If x 2- px + 4 > 0 for all real values of x, then which one of the following is correct?
If 2 + i is a root of the equation x 2- ax + 1 = 0, then the value of a is:
If \(\tan \left( {\frac{α }{2}} \right)\) and \(\tan \left( {\frac{β }{2}} \right)\) are the roots of the equation 8x 2- 26x + 15 = 0, then the value of cos (α + β) will be
