Advertisements
Advertisements
प्रश्न
Write f(x) = x2 + 5x + 4 in completed square form
Advertisements
उत्तर
The given quadratic equation is
f(x) = x2 + 5x + 4
Let y = x2 + 5x + 4
y – 4 = x2 + 5x
`y - 4 + 25/4 = x^2 + 2 xx 5/2 xx x + 25/4`
`y + (25 - 16)/4 = x^2 + 2 xx 5/2 xx x + (5/2)^2`
`y + 9/4 = (x + 5/2)^2`
y = `(x + 5/2)^2 - 9/4`
y = `(x + 5/2)^2 - (3/2)^2`
APPEARS IN
संबंधित प्रश्न
Construct a quadratic equation with roots 7 and −3
A quadratic polynomial has one of its zeros `1 + sqrt(5)` and it satisfies p(1) = 2. Find the quadratic polynomial
If one root of k(x − 1)2 = 5x − 7 is double the other root, show that k = 2 or −25
If the difference of the roots of the equation 2x2 − (a + 1)x + a − 1 = 0 is equal to their product, then prove that a = 2
Find the condition that one of the roots of ax2 + bx + c may be negative of the other
Find the condition that one of the roots of ax2 + bx + c may be reciprocal of the other
If the equations x2 − ax + b = 0 and x2 − ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2(b + f)
Discuss the nature of roots of − x2 + 3x + 1 = 0
Discuss the nature of roots of 4x2 − x − 2 = 0
Discuss the nature of roots of 9x2 + 5x = 0
Solve – x2 + 3x – 2 ≥ 0
Choose the correct alternative:
Find a so that the sum and product of the roots of the equation 2x2 + (a − 3)x + 3a − 5 = 0 are equal is
Choose the correct alternative:
The number of solutions of x2 + |x − 1| = 1 is
Choose the correct alternative:
The equation whose roots are numerically equal but opposite in sign to the roots of 3x2 − 5x − 7 = 0 is
Choose the correct alternative:
If 8 and 2 are the roots of x2 + ax + c = 0 and 3, 3 are the roots of x2 + dx + b = 0, then the roots of the equation x2 + ax + b = 0 are
