If {x^2} + px + q = 0 is the quadratic equati | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$.From the properties of quadratic equations,the sum of roots $a + b = 3$ and the produ

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Given that $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$.From the properties of quadratic equations,the sum of roots $a + b = 3$ and the product of roots $ab = 1$.The roots of the equation ${x^2} + px + q = 0$ are $(a - 2)$ and $(b - 2)$.Sum of roots: $(a - 2) + (b - 2) = -p$$(a + b) - 4 = -p$$3 - 4 = -p \Rightarrow -1 = -p \Rightarrow p = 1$.Product of roots: $(a - 2)(b - 2) = q$$ab - 2(a + b) + 4 = q$$1 - 2(3) + 4 = q$$1 - 6 + 4 = q \Rightarrow q = -1$.Thus,$(p, q) = (1, -1)$.Since this pair is not listed in options $A, B,$ or $C$,the correct answer is $D$.

If ${x^2} + px + q = 0$ is the quadratic equation whose roots are $a - 2$ and $b - 2$,where $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$,then

Similar Questions

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is

$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $8x^2 + 6x = 5$
$II.$ $12y^2 - 22y + 8 = 0$

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

If the product of the roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module