Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by formula method.
5m2 – 4m – 2 = 0
उत्तर
5m2 – 4m – 2 = 0
Comparing the above equation with am2 + bm + c = 0, we get
a = 5, b = – 4, c = – 2
∴ b2 – 4ac = (– 4)2 − 4 × 5 × (– 2)
= 16 + 40
= 56
m = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`
= `((-4) +- sqrt(56))/(2(5))`
= `(4 +- sqrt(4 xx 14))/10`
= `(4 +- 2sqrt(14))/10`
= `(2(2 +- sqrt(14)))/10`
∴ m = `(2 +- sqrt(14))/5`
∴ m = `(2 + sqrt(14))/5` or m = `(2 - sqrt(14))/5`
∴ The roots of the given quadratic equation are `(2 + sqrt(14))/5` and `(2 - sqrt(14))/5`
संबंधित प्रश्न
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
Solve : 7y = -3y2 - 4
Form the quadratic equation if its roots are 5 and 7.
Choose the correct alternative answer for the following sub-questions and write the correct alphabet.
Which of the following quadratic equation has roots – 3 and – 5?
If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’
Roots of a quadratic equation are 5 and – 4, then form the quadratic equation
Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`
Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation
Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0.
One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.
Activity:
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = `square` in the above equation
∴ `"k"(square)^2 - 10 xx square + 3` = 0
∴ `square` – 30 + 3 = 0
∴ 9k = `square`
∴ k = `square`
Determine whether (x – 3) is a factor of polynomial x3 – 19x + 30.
Let P(x) = x3 – 19x + 30
By remainder theorem, `square` will be a factor of P(x), if P(3) = 0
Now, P(3) = `square` – 19 `square` + 30
= `square – square` + 30
= `square – square`
= 0
∵ P(3) = 0
Hence, `square` is a factor of polynomial x3 – 19x + 30.
If the sum of the roots of the quadratic equation x2 + kx + 6 = 0 is 6, then the value of k is ______.
If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.
Since, `square` is a root of equation x2 + 5x + a = 0
∴ Put x = `square` in the equation
⇒ `square^2 + 5 xx square + a` = 0
⇒ `square + square + a` = 0
⇒ `square + a` = 0
⇒ a = `square`
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.
