Advertisements
Advertisements
प्रश्न
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Advertisements
उत्तर
\[Here, a = 1, b = 5, c = - \left( a^2 + a - 6 \right)\]
\[Now, \]
\[D = \left( 5 \right)^2 - 4 \times 1 \times \left[ - \left( a^2 + a - 6 \right) \right]\]
\[ = 25 + 4 a^2 + 4a - 24\]
\[ = 4 a^2 + 4a + 1\]
\[ = \left( 2a + 1 \right)^2\]
\[\therefore x = \frac{- 5 \pm \sqrt{\left( 2a + 1 \right)^2}}{2} \left( x = \frac{- b \pm \sqrt{D}}{2a} \right)\]
\[ = \frac{- 5 + 2a + 1}{2}, \frac{- 5 - 2a - 1}{2}\]
\[ = \frac{2a - 4}{2}, \frac{- 2a - 6}{2}\]
\[ = a - 2, - a - 3\]
APPEARS IN
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 - (a + b + c)x + a = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Which of the following equations has 2 as a root?
(x2 + 1)2 – x2 = 0 has ______.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x(1 – x) – 2 = 0
Solve the equation: 3x2 – 8x – 1 = 0 for x.
