Advertisements
Advertisements
Question
Construct a quadratic equation with roots 7 and −3
Solution
The given roots are 7 and – 3
Let α = 7 and β = – 3
α + β = 7 – 3 = 4
αβ = (7)(– 3) = – 21
The quadratic equation with roots α and β is x2 – (α + β) x + αβ = 0
So the required quadratic equation is
x2 – (4) x + (– 21) = 0
(i.e.,) x2 – 4x – 21 = 0
APPEARS IN
RELATED QUESTIONS
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 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 9x2 + 5x = 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
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 + 6x + 9
Solve 2x2 + x – 15 ≤ 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 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
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
