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2 common monomial 1 diff. Of two squares 1 sum of two cubes1 diff. Of two cubes 2 General trinomial where a=11 general trinomial a greater than 12 si … mplifying rational expressions(with solution po and answer Salamat po)
Guys help me plss i will brainles
B. Multiply and simplify. 1) 7/12 X 4/8 = 2) 10/15 X 2/6= 3) 4/9 X 3/4= 4) 2/3 X 4/7= 5) 5/7 X 2/3= ... Pls sagutan nyo po to kailangan kopo to sa mat … h
Pa answer po please kailangan Lang po
f(x)=x+5 find:f(0),f(-5),f(-3),f(x-1)
Pa answer po please kailangan Lang po
Pa answer po please kailangan Lang po
If the first and the last term of geometric sequence are 6 and 625 what are the two geometric means
A cook has 2 3/4 pounds of ground beef how many quarter pound burgers can he make
Factor The General Trinomial where the A is not 1.8x² - 11x -10 Thanks
solve the given quadratic equations by eextracting square root of. m2=64what is the answer answer and check
Complete the table below. LOCATION Bedroom 1 Bedroom 2 Living Room Dining Room Comfort room Kitchen Laundry Area DIMENSION LENGTH (in meters) WIDTH (i … n meters) TOTAL SURFACE AREA AREA (Square meters)
PAKISAGOT PO NEED KO NAPO BUKAS MAAWA PO KAYO SAAKIN PLEASE
is:3161705292045, 336254 643528 945752 430 980 00812073528495350831678 750325 413473 853638 880874 125divisible by 2,3,4,5,6,8,9,10,11,12(the answer i … n every number will have more than 1 answer)
1). f(x) = 3x - 7 g(x) = 10x - 2 2). f(x) = 11x + 3 g(x) = 3x - 2 3). f(x)= 2-5x g(x) = 5 - 2x 4). f(x) = x-3 h(x) = x + 5 5). f(x) = 5x + 20 ; g(x) … = 7x + 5 6). f9X0 = 15x + 20; g(x) = 7x + 5 7). f(x) = 2-5x g(x) = 5 - 2x 8). f(x) = 3x - 2 g(x) = 2x 9) f(x) = x3
SIMPLIFY THE FOLLOWING.1. 2a+8b______ 62. 10c³d⁸e______4c²d⁵w3. -7(a-b)______21 (a-b)4. 9 (y+6)______15 (y+6)5. 6n_____3+15n6. a-5____5-a7. 3p-6_ … ____3m+98. 5x-15_____9-3x
pa help po. thanks...
given the points A(-1,2) and B(7,8), find the coordinates of the point P on the direct line segment AB that partitions AB in the ratio 1:3. Plot P alo … ng with segment AB
19th term of the arithmetic sequence if a1=25 and d=-2
25th term of the arithmetic sequence if a1=1/2 and d=-3â8
- Math Doubts
- Quadratic equations
- Roots
- Nature
The roots of a quadratic equation are imaginary and distinct if the discriminant of a quadratic equation is negative.
Introduction
When a quadratic equation is expressed as $ax^2+bx+c = 0$ in algebraic form, the discriminant ($\Delta$ or $D$) of the quadratic equation is written as $b^2-4ac$.
The roots or zeros of the quadratic equation in terms of discriminant are written in the following two forms.
$(1).\,\,\,$ $\dfrac{-b+\sqrt{\Delta}}{2a}$
$(2).\,\,\,$ $\dfrac{-b-\sqrt{\Delta}}{2a}$
If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined. However, the square of a negative quantity can be expressed by an imaginary quantity.
For example $\sqrt{\Delta} \,=\, id$
Now, the zeros or roots of the quadratic equation can be written in the following form.
$(1).\,\,\,$ $\dfrac{-b+id}{2a}$
$(2).\,\,\,$ $\dfrac{-b-id}{2a}$
The two roots clearly reveal that the zeros or roots of the quadratic equation are distinct and imaginary.
Example
$5x^2+7x+6 = 0$
Evaluate the discriminant of this quadratic equation.
$\Delta \,=\, 7^2-4 \times 5 \times 6$
$\implies$ $\Delta \,=\, 49-120$
$\implies$ $\Delta \,=\, -71$
Similarly, find the square root of the discriminant.
$\implies$ $\sqrt{\Delta} \,=\, \sqrt{-71}$
$\implies$ $\sqrt{\Delta} \,=\, i\sqrt{71}$
The zeros or roots of the given quadratic equation are given here.
$\,\,\, \therefore \,\,\,\,\,\,$ $x \,=\, \dfrac{-7+i\sqrt{71}}{10}$ and $x \,=\, \dfrac{-7-i\sqrt{71}}{10}$
Therefore, it is proved that the roots are distinct and complex roots if the discriminant of quadratic equation is less than zero.
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