Directions (106-108): Solve the quadratic and answer the following questions. A: $(x-2)^2 = (-3x)^2 + 2^2 + 25x - P$ B: $(10y^2 - 3y + \tfrac{2}{3}) \times 3 + 10y = 0$ One root of equation A is 5. Q106. $\frac{7P}{21} \times 0.2P - 89$ is equal to?

P+2
2P+2
P+1
2P-1

Correct answer: 2P-1

Solution

Since 5 is a root of equation A, substituting x = 5 gives the value of P. After finding P, the required expression simplifies directly to one of the options.

Related IBPS PO Quantitative Aptitude questions

Directions (141-143): Solve the given equations and answer the question below. I. $Ax^2 + 5x + 6 = 0$ II. $By^2 - 13y + 20 = 0$ III. $u^2 + 7u + 12 = 0$ IV. $v^2 - 9v + 20 = 0$ Note: (i) The sum of the coefficients of $x^2$, $x$, $y^2$, and $y$ is -5. (ii) Roots of all the equations are non-imaginary. (iii) Both A and B are positive integers. Find the difference between the larger root of equation IV and the smaller root of equation II.
Q82. Solve both equations and form a new equation in variable 'z' (reduce to the lowest possible factor) using the roots of equations 1 and 2 as per the instructions given below. 1. $2 - \frac{1}{x} + \frac{9}{x^2} = 0$ 2. $(y - 2)^2 = 2\frac{1}{4}$ What will be the new equation if the roots are the highest root of equation 1 and the lowest root of equation 2?
Directions (66–68): Read the following quadratic equations carefully and answer the questions given below. (i) $x\times x - 3x - \sqrt{4x^2} = -6$ (ii) $y^2 - \sqrt{81y^2} = -4\times 5$ (iii) $\dfrac{z^2}{\sqrt{625z^6}} + (4\times 7) = 39z$ (iv) $p^2 - (3\times 5)p = 7\times (-8)$ Q66. Find the L.C.M. of the larger roots of $x$, $y$, $z$, and $p$. A) 840 B) 650 C) 780 D) 980 E) 1010
P and Q are the correct terms of series A and series B respectively. If $R$ is equal to the square of the larger root of the equation $x^2 - 15x = -9^2 + 5^2$, then which of the following statement(s) is/are correct? (i) $Q + R = P$ (ii) $\frac{P}{3} + 15 = R - Q$ (iii) $\sqrt{R} + P = 7Q - 5$ A) Only (i) & (ii) B) Only (ii) & (iii) C) Only (i) D) Only (ii) E) Only (iii)
In each question, two equations numbered (I) and (II) are given. You have to solve both equations and mark the appropriate answer accordingly. (I) x^2 + 5x + 6 = 0 (II) y^2 - 5y + 6 = 0
I. $2x^2 + 17x + 35 = 0 \Rightarrow (2x + 7)(x + 5) = 0 \Rightarrow x = -\frac{7}{2}, -5$ II. $3y^2 + 17y + 24 = 0 \Rightarrow (y + 3)(3y + 8) = 0 \Rightarrow y = -3, -\frac{8}{3}$ Compare $x$ and $y$.

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