Advertisements
Advertisements
प्रश्न
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
विकल्प
Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Advertisements
उत्तर
Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
Explanation:
Sum of roots = `5 + sqrt(7) + 5 - sqrt(7)` = 10,
which is a rational number.
and product of roots = `(5 + sqrt(7)) (5 - sqrt(7))`
= 25 – 7
= 18
which is also a rational number.
APPEARS IN
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
Every quadratic equation has at least one real root.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
