Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Advertisements
उत्तर
Given quadratic equation is 5m2 + 5m – 1 = 0
Comparing with general form ax2 + bx + c = 0, we have
a = 5, b = 5 and c = –1
∴`X=(-b+-sqrt(b^2-4ac))/(2a`
`=(-5+-sqrt(5^2-4(5)(-1)))/(2*5)`
`=(-5+-sqrt(25+20))/10`
`=(-5+-sqrt45)/10`
`=(-5+-3sqrt5)/10`
∴`(-5+3sqrt5)/10`and `(-5-3sqrt5)/10`are the roots of the given equation.
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
If p, q are real and p ≠ q, then show that the roots of the equation (p – q) x2 + 5(p + q) x – 2(p – q) = 0 are real and unequal.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 0.
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
If α, β are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is:
Solve the equation: 3x2 – 8x – 1 = 0 for x.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
