Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
y = x2 + 6x + 9
y = x2 + 6x + 9 ......(3)
Compare this equation with the equation
ax2 + bx + c = 0
We have a = 1, b = 6, c = 9
b2 – 4ac = 62 – 4 × 1 × 9
= 36 – 36
= 0
Since the discriminant is zero the quadratic equation has real and equal roots and therefore the graph touches the x-axis at one point.
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 reciprocal of the other
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 − 3x − 7
Solve 2x2 + x – 15 ≤ 0
Solve – x2 + 3x – 2 ≥ 0
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
