Advertisements
Advertisements
प्रश्न
If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k
उत्तर
Let α and α2 be the root of the equation 3x2 + kx + 81
Here a = 3, b = k, c = 81
α + α2 = `- "k"/3`
3α + 3α2 = – k ...(1)
Product of the roots = `"c"/"a" = 81/3` = 27
α × α2 = 27
α3 = 27 ⇒ α3 = 33
α = 3
Substitute the value of α = 3 in (1)
3(3) + 3(3)2 = – k
9 + 27 = – k
⇒ 36 = – k
∴ k = – 36
The value of k = – 36
APPEARS IN
संबंधित प्रश्न
Determine the quadratic equation, whose sum and product of roots are – (2 – a)2, (a + 5)2
Solve the following quadratic equation by factorization method
3(p2 – 6) = p(p + 5)
Solve the following quadratic equation by factorization method
`2x^2 - x + 1/8` = 0
Solve the following quadratic equation by completing the square method
9x2 – 12x + 4 = 0
A ball rolls down a slope and travels a distance d = t2 – 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet
A garden measuring 12m by 16m is to have a pedestrian pathway that is ‘ω’ meters wide installed all the way around so that it increases the total area to 285 m2. What is the width of the pathway?
A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.
Determine the nature of the roots for the following quadratic equation
15x2 + 11x + 2 = 0
If the roots of (a – b)x2 + (b – c)x + (c – a) = 0 are real and equal, then prove that b, a, c are in arithmetic progression
If a, b are real then show that the roots of the equation (a – b)x2 – 6(a + b)x – 9(a – b) = 0 are real and unequal
