Advertisements
Advertisements
Question
If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a)`x^2-6x+6=0` (b)` x^2+6x+6=0` (c)`x^2-6x-6=0` (d)`x^2+6x+6=0`
Solution
(a)`x^2-6x+6=0`
Given:
Sum of roots = 6
Product of roots = 6
Thus, the equation is:
`x^2-6x+6=0`
APPEARS IN
RELATED QUESTIONS
If one root of the equation` 3x^2-10x+3=0 is 1/3` then the other root is
(a) `-1/3` (b) `1/3` (c)`-3` (d)`3`
Solve `sqrt3x^2+10x-8sqrt3=0`
Solve `4x^2+4bx-(a^2-b^2)=0`
Solve `x^2+5x-(a^2+a-6)=0`
Solve `x^2+6x-(a^2+2a-8)=0`
is the following equation quadratic?
\[\left( x + 2 \right)^2 = 2 x^2\]
Solve the following quadratic equation.
`1/(x + 5) = 1/x^2`
Write the quadratic equation 7 = 4x - x2 in the form of ax2+bx + c = 0.
Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has
In the adjoining fig. `square` ABCD is a trapezium AB || CD and its area is 33 cm2. From the information given in the figure find the lengths of all sides of the `square` ABCD. Fill in the empty boxes to get the solution.
Solution: `square` ABCD is a trapezium.
AB || CD
`"A"(square "ABCD") = 1/2 ("AB" + "CD") xx`______
33 = `1/2 ("x" + 2"x" + 1) xx `______
∴ ______ = (3x + 1) × ______
∴ 3x2 +______ − ______ = 0
∴ 3x(______) + 10(______) = 0
∴ (3x + 10) (______) = 0
∴ (3x + 10) = 0 or ______ = 0
∴ x = `-10/3` or x = ______
But length is never negative.
∴ `"x" ≠ -10/3`
∴ x = ______
AB = ______, CD = ______, AD = BC = ______
