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 − 3x − 7
Advertisements
उत्तर
y = x2 – 3x – 7
y = x2 – 3x – 7 ......(2)
Compare this equation with the equation ax2 + bx + c = 0
We have a = 1, b = – 3, c = – 1
b2 – 4ac = (– 3)2 – 4(1)(– 1)
= 9 + 4
b2 – 4ac = 13 > 0
Since the discriminant is positive the quadratic equation has real and distinct roots and therefore the graph intersect the x-axis at two different points.
APPEARS IN
संबंधित प्रश्न
Construct a quadratic equation with roots 7 and −3
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 negative of the other
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 + 6x + 9
Solve 2x2 + x – 15 ≤ 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:
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:
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 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
