positive roots. [Hint: Multiply by x + 1, which not change the number of positive roots.] 4. Show that the equation x if 5. Find the number of positive roots of the equation x³ + 2x³ – x² +x – 1 = 0. or an 6. From Descartes's rule of signs, conclude that the equation x2" –1 = 0 has 2n – 2 imaginary roots. 7. Without actually obtaining these roots, show that (a) x + 3x +7=0 and (b) x6 – 5x³ – 7x² + 8x + 20 = 0 lo iniog ou both possess imaginary roots. %3D %3D 8. Verify the following assertions. If all the coefficients of an equation are positive (a) and the equation involves no odd powers of x, then all its roots are imaginary. If all the coefficients of an equation are positive [h (b) and all terms involve odd powers of x, then zero is the only real root of the equation. Newton: The Principia Mathematica 8.3 For M.. of The Textbooks of Oughtred spe hea and Harriot wh the the will of the people. The smoldering antag into a conflict of the worst kind, the Great C lusibnsq 8 The Mechanical World:Descartes and Newton 8. (c) An equation with only positive coefficients che cannot have a positive root. noailuaed ro jo Oooiplaiabtylofle sidnin (a) The equation x³+a?x+b² = 0 has one negative and two imaginary roots if b0. (b) The equation x³ – a²x + b² = 0 has one negative root, while the other two roots are either imaginary or both positive. (c) The equation x4 + a²x² + b²x – c² = 0 has just two imaginary roots if c 0. corme 9. Prove that Modi be brur 10. Use Descartes's method to find the solutions of the following quartic equations: (a) x4 - 3x2 + 6x – 2 = 0. [Hint: The sextic Ok* + 17k2 – 36 = 0 has k? = 4 as solution 1 %3D

Q: Add. 4 5/8 + 4 4/7

A:

Q: a) How many students are taking Art?

A: the number of students taking Art if given by 6+10=16

Q: What is the Probability that a student is not taking either class?

A: From the given Venn diagram, it is observed that the number of students who are taking art only is…

Q: Find d(4)H.W dx X3 HiW

A:

Q: Multiply. 3 x-4 3 3 2 X+4

A:

Q: 14 m2a2

A: Total female = 133+43 = 178 Total "did not graduate" = 55+43 = 98 Grand total= (126+55+133+43)  =…

Q: ro In r Evaluate dr. d.x Jo r2+4

A:

Q: 1b+1b

A: Applying  addition operation since terms with same variable  binomial addition

Q: 9 b and c

A: b) We check if the denominator is 0 for any value of x.  2x2+5=0 2x2=-5 x2=-5/2 (not possible) So…

Q: 18 A D. 5x-7

A: Given ,  We have to find value of x

Q: a; = 12, a, = -48, find r and a,

A:

Q: Question 9

A:

Q: 11 35

A:

Q: Letters b, c, d and e.

A:

Q: 9/3 7/3 +. 9.

A:

Q: Table 1,4

A: Independent variables does not relies on other factors and stands alone. Some examples of…

Q: AB 20

A: From the figure, we can see that triangle AXB and triangle AXC are congruent. If they are congruent…

Q: Evaluate P, and 1C7

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.