Solve the following quadratic equation: x^2 - (2b - 1)x + (b^2 - … - Vidyadip

Question

Solve the following quadratic equation: $x^2 - (2b - 1)x + (b^2 - b - 20) = 0$

✓

Answer

$x^2 - (2b - 1)x + (b^2 - b - 20) = 0$
$\Rightarrow x^2 - (2b - 1)x + (b^2 - 5b + 4b - 20) = 0$
$\Rightarrow x^2 - (2b - 1)x + [b(b - 5) + 4(b - 5)] = 0$
$\Rightarrow x^2- (2b - 1)x + (b - 5)(b + 4) = 0$
$\Rightarrow x^2 - (2b - 1)x - (b + 4)x + (b - 5)(b + 4) = 0$
$\Rightarrow x[x - (b - 5)] - (b + 4)[x - (b - 5)] = 0$
$\Rightarrow [x - (b - 5)][x - (b + 4)] = 0$
$\Rightarrow x - (b - 5) = 0$ or $x - (b + 4) = 0$
$\Rightarrow x = b - 5$ or $x = b + 4$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Determine whether the triangle having sides $(a - 1)\ cm$, $2\sqrt{\text{a}}\text{ cm}$ and $(a + 1)\ cm$ is a right angled triangle.

D and E are the points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that:
AD = 8cm, DB = 12cm, AE = 6cm and CE = 9cm, Prove that $\text{BC}=\frac{5}{2}$ DE.

A solid metallic sphere of diameter 28cm is melted and recast into a number of smaller cones, each of diameter 4cm and height 3cm. Find the number of cones so formed.

Draw a circle with center O and radius 3.6 cm. Draw a tangent to the circle from point B at a distance of 7.2 cm from the center of the circle.

In a quadrilateral $ABCD$, given that $\angle\text{A}+\angle\text{D}=90^\circ.$ Prove that $AC^2 + BD^2 = AD^2 + BC^2$.

A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is $6\ cm$ and its height is $4\ cm$. Determine the surface area of the toy. $(\text{Use}\ \pi=3.14)$

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4cm and 3cm.

If $a - b$, $a$ and $b$ are zeros of the polynomial $f(x) = 2x^3- 6x^2 + 5x - 7$, write the value of a.

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

The largest sphere is carved out of a cube of side 10.5cm. Find the volume of the sphere.