Advertisements
Advertisements
प्रश्न
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Advertisements
उत्तर
The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
∴ x = `(-7 +- sqrt((-7)^2 - 4(-1)(-10)))/(2(-1))`
= `(-7 +- sqrt(9))/(-2)`
= `(7 +- 3)/2`
= 5, 2
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
