The positive value of k for which the equations x2 + kx + 64 = 0 and x2 - 8x + k = 0 will both have real roots, is 1. 16 2. 8 3. 12 4. 4

Given, x2 + kx + 64 = 0 ....(1) x2 - 8x + k = 0 ....(2) Comparing x2 + kx + 64 = 0 with ax2 + bx + c = 0 we get, a = 1, b = k and c = 64. We know that, Discriminant (D) = b2 - 4ac = (k)2 - 4 × (1) × (64) = k2 - 256 Since equations has real roots, ⇒ D 0 ⇒ k2 - 256 0 ⇒ k2 256 ⇒ |k| ⇒ |k| 16 ⇒ 16 k -16 Taking only positive value, ⇒ k 16 .........(3) Comparing x2 - 8x + k = 0 with ax2 + bx + c = 0 we get, a = 1, b = -8 and c = k. We know that, Discriminant (D) = b2 - 4ac = (-8)2 - 4 × (1) × (k) = (64) - 4k Since equations has real roots, ⇒ D 0 ⇒ 64 - 4k 0 ⇒ 4k 64 ⇒ k ⇒ k 16 .........(4) From (3) and (4), we get : ⇒ k = 16. Hence, option 1 is the correct option.

View Answer Bookmark Now

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2

View Answer Bookmark Now

If 3 is a root of the quadratic equation x² - px + 3 = 0, then p is equal to:
4
3
5
2

View Answer Bookmark Now

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal, then the value of k is:
2
8
4
none of these

View Answer Bookmark Now

Mathematics

The positive value of k for which the equations x² + kx + 64 = 0 and x² - 8x + k = 0 will both have real roots, is
16
8
12
4

Quadratic Equations

Related Questions

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2

If 3 is a root of the quadratic equation x² - px + 3 = 0, then p is equal to:
4
3
5
2

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal, then the value of k is:
2
8
4
none of these

Mathematics

The positive value of k for which the equations x2 + kx + 64 = 0 and x2 - 8x + k = 0 will both have real roots, is168124

Quadratic Equations

Related Questions

If the equation, x2 - ax + 1 = 0 has two distinct and real roots, then:|a| ≥ 2|a| ≤ 2|a| > 2|a| < 2

If 3 is a root of the quadratic equation x2 - px + 3 = 0, then p is equal to:4352

If the roots of the quadratic equation 2x2 + 8x + k = 0 are equal, then the value of k is:284none of these

The positive value of k for which the equations x² + kx + 64 = 0 and x² - 8x + k = 0 will both have real roots, is
16
8
12
4

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2

If 3 is a root of the quadratic equation x² - px + 3 = 0, then p is equal to:
4
3
5
2

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal, then the value of k is:
2
8
4
none of these