Advertisements
Advertisements
प्रश्न
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`
उत्तर
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = 3 in the above equation
∴ k(3)2 – 10 × 3 + 3 = 0
∴ 9k – 30 + 3 = 0
∴ 9k = 27
∴ k = `27/9` = 3
APPEARS IN
संबंधित प्रश्न
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
Solve : 7y = -3y2 - 4
If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find the values of (i) `α^2+β^2` (ii) `α^3+β^3`
Form the quadratic equation if the roots are 3 and 8.
Solve the quadratic equation : 3x4 - 13x2 +10 = 0.
Convert the following equations into simultaneous equations and solve:
`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`
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?
Write the roots of following quadratic equation.
(p – 5) (p + 3) = 0
If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`
Solve the following quadratic equation.
`1/(4 - "p") - 1/(2 + "p") = 1/4`
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 roots of the quadratic equation x2 + 12x + a = 0 are real and equal, then find the value of a.
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.