Question
Solve the following quadratic equations by factorization:
$3x^2 = -11x - 10$
$3x^2 = -11x - 10$
✓
Answer
$3x^2 = -11x - 10$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\begin{cases}\because3\times10=30\\\therefore30=5\times6\\11=5+6\end{cases}$
$\Rightarrow 3x^2 + 6x + 5x + 10 = 0$
$\Rightarrow 3x(x + 2) + 5(x + 2) = 0$
$\Rightarrow (x + 2)(3x + 5) = 0$
Either $x + 2 = 0$, then $x = -2$
Or $3x + 5 = 0$. then $3x = -5$
$\Rightarrow\text{x}=\frac{-5}{3}$
$\therefore$ Roots are $x = -2$, $\frac{-5}{3}$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\Rightarrow 3x^2 + 11x + 10 = 0$
$\begin{cases}\because3\times10=30\\\therefore30=5\times6\\11=5+6\end{cases}$
$\Rightarrow 3x^2 + 6x + 5x + 10 = 0$
$\Rightarrow 3x(x + 2) + 5(x + 2) = 0$
$\Rightarrow (x + 2)(3x + 5) = 0$
Either $x + 2 = 0$, then $x = -2$
Or $3x + 5 = 0$. then $3x = -5$
$\Rightarrow\text{x}=\frac{-5}{3}$
$\therefore$ Roots are $x = -2$, $\frac{-5}{3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Amir Enterprise purchased chocolate sauce bottles and paid GST of Rs. 3800. He sold those bottles to Akbari Bros. and collected GST of Rs. 4100. Mayank Food Corner purchased these bottles from Akabari Bros and paid GST of Rs. 4500. Find the amount of GST payable at every stage of trading and hence find payable CGST and SGST.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
$x^2 + 3x - 10$
→$x^2 + 3x - 10$
Solve the following quadratic equation:$4x^2 - 9x = 100$
→If $5 \sin \theta-12 \cos \theta=0$, find the values of $\sec \theta$ and $\operatorname{cosec} \theta$..
→Mrs. Sita invested ₹ 92,124 in shares of face value ₹ 10 each at ₹ 90 market value. She paid 2 % brokerage and 18 % GST on it. Company declared a dividend of 60 % on then. Find her dividend.
Three cubes of a metal whose edges are in the ratio $3 : 4 : 5$ are melted and converted into a single cube whose diagonal is $12\sqrt{3}\text{cm}.$ Find the edges of the three cubes.
→A sector of a circle with radius 10 cm has central angle 72°. Find the area of the sector $(\pi=3.14)$
→In the given figure, ABCD is a trapezium with $\text{AB}||\text{DC},\text{AB}=18\text{cm}$ DC = 32cm and the distance between AB and DC is 14cm. Circles of equal radii 7cm with centres A, B, C and D have been drawn. Then find the area of the shaded region.$\Big(\text{Use }\pi=\frac{22}{7}\Big)$
→In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan \alpha=\frac{5}{12}$
→$\tan \alpha=\frac{5}{12}$
ABCD is a rectangle formed by points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P, Q, R and S be the midpoints of AB, BC, CD and DA respectively, show that PQRS is a rhombus.