Advertisements
Advertisements
प्रश्न
Find the condition that one of the roots of ax2 + bx + c may be negative of the other
Advertisements
उत्तर
The given quadratic equation is
ax2 + bx + c = 0 ......(1)
Let α and β be the roots of the equation (1) then
Sum of the roots α + β = 0 .....(2)
Product of the roots αβ = 0 ......(3)
Given one root is the negative of the other
β = – α
(2) ⇒ α + (– α) = `- "b"/a"`
0 = `- "b"/a"`
⇒ b = 0
(3) ⇒ α(– α) = `"c"/"a"`
– α2 = `"c"/"a"`
Hence the required condition is b = 0
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 α and β are the roots of the quadratic equation `x^2 + sqrt(2)x + 3` = 0, form a quadratic polynomial with zeroes `1/α, 1/β`
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 thrice 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 4x2 − x − 2 = 0
Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x2 + x + 2
Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x2 − 3x − 7
Write f(x) = x2 + 5x + 4 in completed square form
Solve – x2 + 3x – 2 ≥ 0
Choose the correct alternative:
If a and b are the roots of the equation x2 − kx + 16 = 0 and satisfy a2 + b2 = 32, then the value of k is
Choose the correct alternative:
The number of solutions of x2 + |x − 1| = 1 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
Choose the correct alternative:
If a and b are the real roots of the equation x2 − kx + c = 0, then the distance between the points (a, 0) and (b, 0) is
Choose the correct alternative:
The number of roots of (x + 3)4 + (x + 5)4 = 16 is
