Advertisements
Advertisements
प्रश्न
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
विकल्प
x2 – px + p = 0
x2 – (p + 1)x + p = 0
x2 + (p + 1)x + p = 0
x2 – px + p + 1= 0
Advertisements
उत्तर
Let p be a prime number. The quadratic equation having its roots as factors of p is `underline(bb(x^2 - (p + 1)x + p = 0)`.
Explanation:
Since p is a prime factor
Factors of p = 1, p
Thus, we need to find quadratic equation with roots 1 and p
Required quadratic equation is x2 – (Sum of roots)x + Product of roots = 0
x2 – (1 + p)x + (1 × p) = 0
x2 – (1 + p)x + p = 0
APPEARS IN
संबंधित प्रश्न
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the value(s) of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
